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Theory and Simulation of Random Phenomena: Mathematical Foundations and Physical Applications

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Theory and Simulation of Random Phenomena: Mathematical Foundations and Physical Applications

4.85 63,343 ratings · 1,886 reviews
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Overview: The purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.

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Topics & Genres

Pages 235
Language Eng
Publisher Springer
Published June 14, 2018
ISBN 40855073
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Ettore Vitali
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Ettore Vitali
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Ettore Vitali is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Ettore Vitali can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Carol Baker
Carol Baker September 11, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Mark Diaz
Mark Diaz June 08, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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Barbara Clark April 13, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Betty Wright
Betty Wright November 26, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Emily Hernandez
Emily Hernandez May 25, 2025
Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. A fair 3 stars.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Jacob Baker
Jacob Baker April 16, 2024
A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perhaps more aligned with a different audience's tastes.
Barbara Sanchez
Barbara Sanchez March 14, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Dorothy Lewis February 21, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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Laura Robinson January 28, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Anthony Wilson
Anthony Wilson March 25, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Linda Martin
Linda Martin May 18, 2025
An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
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Donald Miller January 23, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Ashley Thompson
Ashley Thompson April 04, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Laura  Parker
Laura Parker July 24, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Michael Hill
Michael Hill March 05, 2025
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
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Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
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William Baker May 14, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
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Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Eric Gomez
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
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A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Richard Evans
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Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Richard Brown
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Daniel Taylor
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Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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George Wright February 24, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Ryan Phillips
Ryan Phillips June 29, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
John Scott
John Scott February 23, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Laura Rodriguez
Laura Rodriguez February 28, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Andrew Smith
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Joseph Martin
Joseph Martin April 12, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Nancy Williams
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A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average.
Emily Ramirez
Emily Ramirez January 01, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Michelle Thomas
Michelle Thomas November 26, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Thomas Rivera
Thomas Rivera April 12, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Thomas Lee
Thomas Lee January 02, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Cynthia Scott
Cynthia Scott October 25, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Karen Lee
Karen Lee July 07, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Deborah Perez
Deborah Perez July 07, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Joseph Mitchell
Joseph Mitchell November 22, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
George Carter
George Carter September 19, 2025
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
Nancy  Davis
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Joshua Wilson
Joshua Wilson September 22, 2024
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Margaret Hill
Margaret Hill October 03, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Linda Clark
Linda Clark August 28, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Susan Torres
Susan Torres August 30, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Eric Evans
Eric Evans November 20, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Kevin Gomez
Kevin Gomez October 25, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Matthew Smith
Matthew Smith January 14, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Margaret Wright
Margaret Wright March 03, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Sharon Martin
Sharon Martin December 18, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Barbara Sanchez
Barbara Sanchez November 16, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Jennifer Mitchell
Jennifer Mitchell November 03, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Melissa Allen
Melissa Allen December 19, 2024
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
John Torres
John Torres March 28, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Michael Lewis
Michael Lewis April 24, 2024
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Matthew Collins
Matthew Collins December 22, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Kimberly Brown
Kimberly Brown May 13, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Brian Miller
Brian Miller June 17, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Anthony Wilson
Anthony Wilson September 07, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Ashley Ramirez
Ashley Ramirez March 12, 2025
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
Kenneth Brown
Kenneth Brown February 04, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Barbara Johnson
Barbara Johnson March 18, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Joshua Young
Joshua Young March 05, 2024
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Emily Hernandez
Emily Hernandez December 10, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Ryan Hall
Ryan Hall October 05, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Edward Edwards
Edward Edwards March 10, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Margaret White
Margaret White May 27, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Joshua Reyes
Joshua Reyes February 28, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Edward Thomas
Edward Thomas August 30, 2025
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
Kimberly Brown
Kimberly Brown April 10, 2024
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Andrew Young
Andrew Young July 07, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Andrew Lee
Andrew Lee April 19, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Ashley Gonzalez
Ashley Gonzalez February 03, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Christopher Jones
Christopher Jones February 20, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Amanda Wilson
Amanda Wilson June 24, 2025
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Matthew Evans
Matthew Evans February 06, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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Kimberly Cruz September 02, 2025
Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
Jessica King
Jessica King April 20, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Jacob Hill
Jacob Hill January 28, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Kenneth Flores
Kenneth Flores October 17, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Karen Phillips
Karen Phillips June 02, 2025
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
Donna Walker
Donna Walker June 29, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Nancy Young
Nancy Young July 01, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Kevin Diaz
Kevin Diaz August 23, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Laura Campbell
Laura Campbell September 04, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Christopher Clark
Christopher Clark October 31, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Joseph Mitchell
Joseph Mitchell August 28, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Rebecca Edwards
Rebecca Edwards September 03, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Patricia Garcia
Patricia Garcia March 21, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
David Lopez
David Lopez October 27, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Donald Allen
Donald Allen October 28, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Gary Allen
Gary Allen November 13, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Nancy King
Nancy King April 04, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Kevin Moore
Kevin Moore December 15, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Cynthia Anderson
Cynthia Anderson April 21, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Nancy Young
Nancy Young November 20, 2024
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
Kimberly Cruz
Kimberly Cruz September 08, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Michelle Thomas
Michelle Thomas July 26, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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