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020 _a9783031427916
_9978-3-031-42791-6
024 7 _a10.1007/978-3-031-42791-6
_2doi
050 4 _aQA273.A1-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
100 1 _aGovindan, T. E.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_979788
245 1 0 _aTrotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications
_h[electronic resource] /
_cby T. E. Govindan.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXIX, 311 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _a1 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.
520 _aThis 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.
650 0 _aProbabilities.
_965724
650 0 _aMathematical analysis.
_964178
650 0 _aSystem theory.
_966519
650 0 _aControl theory.
_968675
650 1 4 _aProbability Theory.
_967428
650 2 4 _aAnalysis.
650 2 4 _aSystems Theory, Control.
_968676
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031427909
776 0 8 _iPrinted edition:
_z9783031427923
776 0 8 _iPrinted edition:
_z9783031427930
856 4 0 _uhttps://doi.org/10.1007/978-3-031-42791-6
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c61228
_d61228