Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications
This research monograph brings together, for the first time, the varied literature on Yosida approximations of shastic 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 shastic stability and shastic 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 shastic 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 shastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in shastic processes.

1124442396
Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications
This research monograph brings together, for the first time, the varied literature on Yosida approximations of shastic 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 shastic stability and shastic 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 shastic 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 shastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in shastic processes.

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Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications

Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications

by T. E. Govindan
Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications

Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications

by T. E. Govindan

Overview

This research monograph brings together, for the first time, the varied literature on Yosida approximations of shastic 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 shastic stability and shastic 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 shastic 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 shastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in shastic processes.

Product Details

ISBN-13: 9783319456829
Publisher: Springer International Publishing
Publication date: 11/12/2016
Series: Probability Theory and Stochastic Modelling , #79
Edition description: 1st ed. 2016
Pages: 407
Product dimensions: 6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1 Introduction and Motivating Examples. - 2 Mathematical Machinery. - 3 Trotter-Kato Approximations of Shastic Differential Equations. - 4 trotter-Kato Approximations of Shastic Differential Equations in UMD Banach Spaces. - 5 Applications to Shastic Stability. - 6 Applications to Shastic Optimal Control. - Appendix A: Nuclear and Hilbert-Schmidt Operators. - Appendix B: Convergence of Analytic Semigroups. - Appendix C: The Pettis Measurability Theorem. - Appendix D: R-Boundedness and Y-Boundedness. - Appendix E: The Feynman-Kac Formula. - Bibliograpical Notes and Remarks. - Bibliography
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