Authors:
- First book ever published to systematically introduce Yosida approximations and their applications
- Compiles results from the literature spanning more than 35 years
- Most of the results presented are an outgrowth of the author’s own research
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 79)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
About this book
This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces.
The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launchesthe reader into the main discussion of the monograph, namely, Yosida approximations of SDEs, Yosida approximations of SDEs with Poisson jumps, and their applications. Most of the results considered in the main chapters appear for the first time in a book form, and contain illustrative examples on stochastic partial differential equations. The key steps are included in all proofs, especially the various estimates, which help the reader to get a true feel for the theory of Yosida approximations and their use.
This work is intended for researchers and graduate students in mathematics specializing in probability theory and will appeal to numerical analysts, engineers, physicists and practitioners in finance who want to apply the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in stochastic processes.
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Authors and Affiliations
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National Polytechnic Institute, Mexico City, Mexico
T. E. Govindan
Bibliographic Information
Book Title: Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications
Authors: T. E. Govindan
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-319-45684-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-45682-9Published: 18 November 2016
Softcover ISBN: 978-3-319-83347-7Published: 28 June 2018
eBook ISBN: 978-3-319-45684-3Published: 11 November 2016
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XIX, 407
Topics: Probability Theory and Stochastic Processes, Partial Differential Equations, Control and Systems Theory