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Stochastic Differential Equations and Applications (Dover Books on Mathematics)

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Book Details

  • Author: Avner Friedman

  • Publisher: Dover

  • Binding: Paperback

  • Number of Pages: 560

  • ISBN: 9780486453590

  • Languages: English

  • Dimensions: 8.4 x 5.6 x 1.3 inches


About The Book

"Stochastic Differential Equations and Applications" by Avner Friedman provides a comprehensive exploration of stochastic differential equations, covering both the theory and practical applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, this book consolidates foundational theory and selected advanced topics into a single accessible text.

The first part of the book delves into the essential components of stochastic processes, including:

  • Markov processes and Brownian motion.

  • Stochastic integrals and stochastic differential equations.

  • Relationships between elliptic and parabolic partial differential equations and their connection to stochastic differential equations.

  • The Cameron-Martin-Girsanov theorem, a key result in stochastic analysis.

  • Asymptotic estimates for solutions, concluding with an exploration of recurrent and transient solutions.

The second volume begins with foundational results in partial differential equations, progressing to discussions on topics such as:

  • Nonattainability, stability, and spiraling of solutions.

  • The Dirichlet problem for degenerate elliptic equations.

  • Small random perturbations of dynamical systems.

  • Fundamental solutions of degenerate parabolic equations.

The final chapters cover advanced concepts such as stopping time problems, stochastic games, and stochastic differential games. At the end of each chapter, problems are provided to test the reader's understanding. The book is accessible to those with a basic knowledge of elementary probability theory, making it a suitable resource for both students and professionals.

This text is an essential reference for anyone looking to deepen their understanding of stochastic processes, control theory, and partial differential equations.