Stochastic processes
Author(s)
Bibliographic Information
Stochastic processes
（Probability and its applications）
Birkhäuser , Springer, c2017
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Note
Includes bibliographical references (p. 615-622) and index
"Original Russian edition published by LAN Publishing, St. Petersburg, 2013"--T.p. verso
Description and Table of Contents
Description
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.
Table of 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.
by "Nielsen BookData"
