Applied Stochastic Analysis by Miranda Holmes-Cerfon

Applied Stochastic Analysis by Miranda Holmes-Cerfon

This textbook introduces the major ideas of stochastic analysis with a view to modeling or simulating systems involving randomness. Suitable for students and researchers in applied mathematics and related disciplines, this book prepares readers to solve concrete problems arising in physically motivated models. The author's practical approach avoids measure theory while retaining rigor for cases where it helps build techniques or intuition. Topics covered include Markov chains (discrete and continuous), Gaussian processes, Ito calculus, and stochastic differential equations and their associated PDEs. We ask questions such as: How does probability evolve? How do statistics evolve? How can we solve for time-dependent quantities such as first-passage times? How can we set up a model that includes fundamental principles such as time-reversibility (detailed balance)? How can we simulate a stochastic process numerically? Applied Stochastic Analysis invites readers to develop tools and insights for tackling physical systems involving randomness. Exercises accompany the text throughout, with frequent opportunities to implement simulation algorithms. A strong undergraduate background in linear algebra, probability, ODEs, and PDEs is assumed, along with the mathematical sophistication characteristic of a graduate student.

Miranda Holmes-Cerfon, University of British Columbia, Vancouver, BC, Canada

SKU	Unavailable
ISBN 13	9781470478391
ISBN 10	1470478390
Title	Applied Stochastic Analysis
Author	Miranda Holmes-Cerfon
Series	Courant Lecture Notes
Condition	Unavailable
Binding Type	Paperback
Publisher	American Mathematical Society
Year published	2024-11-01
Number of pages	244
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.