04426nam a22005535i 4500 978-3-031-42791-6 DE-He213 20251030112606.0 cr nn 008mamaa 240701s2024 sz | s |||| 0|eng d 9783031427916 978-3-031-42791-6 10.1007/978-3-031-42791-6 doi QA273.A1-274.9 PBT bicssc PBWL bicssc MAT029000 bisacsh PBT thema PBWL thema Govindan, T. E. author. aut http://id.loc.gov/vocabulary/relators/aut 79788 Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications [electronic resource] / by T. E. Govindan. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XIX, 311 p. 1 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 1 Introduction and Motivating Examples -- 2 Mathematical Machinery -- 3 Trotter-Kato Approximations of Stochastic Differential Equations -- 4 Trotter-Kato Approximations of Stochastic Differential Equations in UMD Banach Spaces -- 6 Applications to Stochastic 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 γ-Boundedness -- Appendix E: The Feynman-Kac Formula -- Bibliographical Notes and Remarks -- Bibliography. This is the first comprehensive book on Trotter-Kato approximations of stochastic differential equations (SDEs) in infinite dimensions and applications. This research monograph brings together the varied literature on this topic since 1985 when such a study was initiated. The author provides a clear and systematic introduction to the theory of Trotter-Kato approximations of SDEs and also presents its applications to practical topics such as stochastic stability and stochastic optimal control. The theory assimilated here is developed slowly and methodically in digestive pieces. The book begins with a motivational chapter introducing several different models that highlight the importance of the theory on abstract SDEs that will be considered in the subsequent chapters. The author next introduces the necessary mathematical background and then leads the reader into the main discussion of the monograph, namely, the Trotter-Kato approximations of many classes of SDEs in Hilbert spaces, Trotter-Kato approximations of SDEs in UMD Banach spaces and some of their applications. Most of the results presented in the main chapters appear for the first time in a book form. The monograph also contains many illustrative examples on stochastic partial differential equations and one in finance as an application of the Trotter-Kato formula. The key steps are included in all proofs which will help the reader to get a real insight into the theory of Trotter-Kato approximations and its use. This book is intended for researchers and graduate students in mathematics specializing in probability theory. It will also be useful to numerical analysts, engineers, physicists and practitioners who are interested in applying the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is accessible to a wider audience including non-specialists in stochastic processes. Probabilities. 65724 Mathematical analysis. 64178 System theory. 66519 Control theory. 68675 Probability Theory. 67428 Analysis. Systems Theory, Control. 68676 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031427909 Printed edition: 9783031427923 Printed edition: 9783031427930 https://doi.org/10.1007/978-3-031-42791-6 ZDB-2-SMA ZDB-2-SXMS 61228 61228