Applied Stochastic Analysis: 33 (Courant Lecture Notes) - Softcover

Holmes-Cerfon, Miranda

Softcover

ISBN 10: 1470478390 ISBN 13: 9781470478391

Publisher: American Mathematical Society, 2024

Synopsis

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.

About this title

About the Author

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

Edition details

• Publisher: American Mathematical Society
• Publication date: 2024
• Language: English
• ISBN 10: 1470478390
• ISBN 13: 9781470478391
• Binding: Paperback
• Number of pages: 244