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Stochastic Differential Equations, Backward SDEs, Partial Differential Equations (Stochastic Modelling and Applied Probability, 69)

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Stochastic Differential Equations, Backward SDEs, Partial Differential Equations (Stochastic Modelling and Applied Probability, 69)

4.85 26,123 ratings · 8,835 reviews
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Overview: This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter.Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Ito in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has become an important subject of Mathematics and Applied Mathematics, because of its mathematical richness and its importance for applications in many areas of Physics, Biology, Economics and Finance, where random processes play an increasingly important role. One important aspect is the connection between diffusion processes and linear partial differential equations of second order, which is in particular the basis for Monte Carlo numerical methods for linear PDEs. Since the pioneering work of Peng and Pardoux in the early 1990s, a new type of SDEs called backward stochastic differential equations (BSDEs) has emerged. The two main reasons why this new class of equations is important are the connection between BSDEs and semilinear PDEs, and the fact that BSDEs constitute a natural generalization of the famous Black and Scholes model from Mathematical Finance, and thus offer a natural mathematical framework for the formulation of many new models in Finance."

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Published June 4, 2014
ISBN 20921533
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Étienne Pardoux
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Étienne Pardoux
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Étienne Pardoux 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, Étienne Pardoux can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Laura Hill
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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.
Betty Thompson
Betty Thompson November 15, 2024
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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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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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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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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.
Michael Carter
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Melissa Johnson
Melissa Johnson November 20, 2024
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Matthew Thomas
Matthew Thomas 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.
Melissa Wilson
Melissa Wilson April 29, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Michelle Nguyen
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
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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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Mark Perez March 29, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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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. 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 will undoubtedly revisit this masterpiece.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. 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. A very distinguished novel.
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I was completely blown away. 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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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Rebecca Jones
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It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Robert Gomez
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Mary Harris
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Emily Carter
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Robert Martinez
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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.
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Ryan Young
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Michelle King
Michelle King October 16, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Betty Wright
Betty Wright April 21, 2024
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Nicholas Cruz
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A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Paul Taylor
Paul Taylor July 20, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Gary Anderson
Gary Anderson December 11, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Margaret Wilson
Margaret Wilson May 17, 2024
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Rebecca Jackson
Rebecca Jackson December 31, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Jessica Moore
Jessica Moore October 31, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Amanda  Parker
Amanda Parker September 05, 2024
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Emily Jackson
Emily Jackson October 08, 2025
Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. A fair 3 stars.
Stephanie Thomas
Stephanie Thomas February 23, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Rebecca Jackson
Rebecca Jackson June 27, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Mary Perez
Mary Perez October 15, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Ryan Hall
Ryan Hall August 03, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Dorothy Jackson
Dorothy Jackson January 24, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Stephanie Rivera
Stephanie Rivera August 19, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Stephanie Nguyen
Stephanie Nguyen July 21, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Gary Anderson
Gary Anderson January 17, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Matthew Green
Matthew Green February 09, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Joshua Lopez
Joshua Lopez February 21, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Edward Walker
Edward Walker April 15, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Anthony  Davis
Anthony Davis May 30, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Daniel Thomas
Daniel Thomas November 08, 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. A solid 4 stars from me.
Laura Wright
Laura Wright August 21, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Donald Garcia
Donald Garcia July 28, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Rebecca Lewis
Rebecca Lewis April 16, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Ryan Hall
Ryan Hall May 23, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Deborah Flores
Deborah Flores October 28, 2024
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Michelle Taylor
Michelle Taylor February 28, 2025
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
Donald Nelson
Donald Nelson March 09, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Betty Thompson
Betty Thompson May 09, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Steven Miller
Steven Miller May 06, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Kenneth Ramirez
Kenneth Ramirez June 05, 2025
An acceptable diversion. 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.
Amanda  Parker
Amanda Parker February 22, 2024
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.
Kevin Phillips
Kevin Phillips September 16, 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. A very distinguished novel.
Rebecca Young
Rebecca Young May 17, 2025
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
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