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Stochastic Processes: A Survey of the Mathematical Theory (Applied Mathematical Sciences, 23) (Volume 0)

Stochastic Processes: A Survey of the Mathematical Theory (Applied Mathematical Sciences)

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Stochastic Processes: A Survey of the Mathematical Theory (Applied Mathematical Sciences, 23) (Volume 0)

Stochastic Processes: A Survey of the Mathematical Theory (Applied Mathematical Sciences)

4.85 85,768 ratings · 42,664 reviews
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Overview: This book is the result of lectures which I gave dur- ing the academic year 1972-73 to third-year students a Aarhus University in Denmark. The purpose of the book, as of the lectures, is to survey some of the main themes in the modern theory of stochastic processes. In my previous book Probability: ! survey of the mathe- matical theory I gave a short overview of classical proba- bility mathematics, concentrating especially on sums of inde- pendent random variables. I did not discuss specific appli- cations of the theory; I did strive for a spirit friendly to application by coming to grips as fast as I could with the major problems and techniques and by avoiding too high levels of abstraction and completeness. At the same time, I tried to make the proofs both rigorous and motivated and to show how certain results have evolved rather than just presenting them in polished final form. The same remarks apply to this book, at least as a statement of intentions, and it can serve as a sequel to the earlier one continuing the story in the same style and spirit. The contents of the present book fall roughly into two parts. The first deals mostly with stationary processes, which provide the mathematics for describing phenomena in a steady state overall but subject to random fluctuations. Chapter 4 is the heart of this part.

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Published September 1, 1977
ISBN 3418231
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J. Lamperti
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J. Lamperti writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. J. Lamperti lives with their spouse and a very vocal rescue cat.

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Lisa Harris
Lisa Harris January 06, 2024
An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
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A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
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Richard Lee March 04, 2024
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Eric Robinson
Eric Robinson January 27, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Eric Diaz
Eric Diaz January 26, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Carol Turner
Carol Turner November 05, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Laura Campbell March 25, 2025
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. 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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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.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Eric Campbell
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Amanda Allen
Amanda Allen July 13, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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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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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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A profoundly satisfying read. 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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I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
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A profoundly satisfying read. 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. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Steven Ramirez
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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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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Steven Gonzalez
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Daniel Rodriguez June 05, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Jennifer Martin
Jennifer Martin February 05, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Jessica Green
Jessica Green March 11, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Susan Wilson June 25, 2025
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.
Emily Carter
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Betty Baker February 06, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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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.
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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.
Carol Brown
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Karen Nelson November 27, 2024
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
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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 very distinguished novel.
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Rebecca Allen September 01, 2025
Took a moment to build, but the payoff was spectacular. 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 pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Linda Roberts
Linda Roberts August 05, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Sarah Rivera
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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.
Edward Edwards
Edward Edwards September 24, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Dorothy Jones
Dorothy Jones April 09, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Richard Lee
Richard Lee January 10, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Jacob Thomas
Jacob Thomas March 17, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Mark Thompson
Mark Thompson December 06, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Richard Jackson
Richard Jackson May 13, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Eric Young
Eric Young January 21, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Ashley  Parker
Ashley Parker December 15, 2025
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Jessica Martin
Jessica Martin May 26, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Thomas Jones
Thomas Jones September 18, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Kevin Perez
Kevin Perez December 27, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Nicholas Green
Nicholas Green November 23, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Thomas Wright
Thomas Wright May 09, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Jessica Diaz
Jessica Diaz December 31, 2024
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Sandra Hall
Sandra Hall October 20, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Betty Flores
Betty Flores September 26, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Kevin Cruz
Kevin Cruz January 21, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Sarah Taylor
Sarah Taylor June 20, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Jacob Jackson
Jacob Jackson May 16, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Charles Williams
Charles Williams February 21, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Brian Perez
Brian Perez December 27, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Amanda White
Amanda White July 26, 2024
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. A fair 3 stars.
Joseph Jones
Joseph Jones November 14, 2025
An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
Donna Garcia
Donna Garcia June 25, 2024
A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
Kenneth Torres
Kenneth Torres May 23, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Kimberly Clark
Kimberly Clark April 20, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Brian Johnson
Brian Johnson May 03, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
William Turner
William Turner November 24, 2024
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.
Anthony Young
Anthony Young April 18, 2025
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Amanda Allen
Amanda Allen February 05, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Steven Carter
Steven Carter April 04, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Robert Robinson
Robert Robinson May 18, 2024
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
Joseph Baker
Joseph Baker May 31, 2025
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Michael Allen
Michael Allen August 23, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Laura Campbell
Laura Campbell July 26, 2025
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.
Betty Mitchell
Betty Mitchell December 13, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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