Yosida Approximations Of Stochastic Differential Equations In Infinite Dimensions And Applications (probability Theory And Stochastic Modelling)
by T. E. Govindan /
2016 / English / PDF
4.6 MB Download
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.
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.
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.
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.