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Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications

  • T. E. ¬†Govindan

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 79)

Table of contents

  1. Front Matter
    Pages i-xix
  2. T. E. Govindan
    Pages 1-10
  3. T. E. Govindan
    Pages 11-68
  4. T. E. Govindan
    Pages 241-331
  5. T. E. Govindan
    Pages 333-367
  6. Back Matter
    Pages 369-407

About this book

Introduction

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 launches the 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.  

 

 

 

Keywords

McKean-Vlasov evolution equations Yosida approximations existence and uniqueness of solutions mild and strong solutions stochastic differential equations in infinite dimensions weak convergence of induced probability measures

Authors and affiliations

  • T. E. ¬†Govindan
    • 1
  1. 1.National Polytechnic InstituteMexico CityMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-45684-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-45682-9
  • Online ISBN 978-3-319-45684-3
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
  • Buy this book on publisher's site
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