Stochastic processes / by Andrei N Borodin.

Format:

Book

Author/Creator:

Borodin, A. N., Author.

Series:

Probability and Its Applications, 2297-0371

Language:

English

Subjects (All):

Probabilities.

Probability Theory and Stochastic Processes.

Local Subjects:

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (XIV, 626 p. 1 illus.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.

Summary:

This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.

Contents:

Preface

Notations

Basic facts

Stochastic calculus

Distributions of functionals of Brownian motion

Diffusion processes

Brownian local time

Diffusions with jumps

Invariance principle for random walks and local times

Appendix 1. Heat transfer problem

Appendix 2. Special functions

Appendix 3. Inverse Laplace transforms

Appendix 4. Differential equations and their solutions

Appendix 5. Examples of transformations of measures associated with diffusion processes

Appendix 6. Formulae for n-fold differentiation

Bibliography

Subject index.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-62310-9