Applied Stochastic Analysis
eBook - PDF

Applied Stochastic Analysis

  1. 252 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Applied Stochastic Analysis

About this book

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, Itô 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.

Table of contents

  1. Cover
  2. Title page
  3. Copyright
  4. Contents
  5. Preface
  6. Chapter 1. Introduction
  7. Chapter 2. Markov Chains (I)
  8. Chapter 3. Markov Chains (II): Detailed Balance and Markov Chain Monte Carlo (MCMC)
  9. Chapter 4. Continuous-Time Markov Chains
  10. Chapter 5. Gaussian Processes and Stationary Processes
  11. Chapter 6. Brownian Motion
  12. Chapter 7. Stochastic Integration
  13. Chapter 8. Stochastic Differential Equations
  14. Chapter 9. Numerically Solving SDEs
  15. Chapter 10. Forward and Backward Equations for SDEs
  16. Chapter 11. Some Applications of the Backward Equation
  17. Chapter 12. Detailed Balance, Symmetry, and Eigenfunction Expansions
  18. Chapter 13. Asymptotic Analysis of SDEs
  19. Appendix A. Appendix
  20. Bibliography
  21. Index
  22. Back Cover

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Yes, you can access Applied Stochastic Analysis by Miranda Holmes-Cerfon in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.