04061nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001900153072001600172072001700188072002300205072001500228072001600243100007700259245015400336250001800490264007500508300004300583336002600626337002600652338003600678347002400714505057200738520191501310650001903225650002703244650001903271650002003290650002403310650001403334650002903348710003403377773002603411776003603437776003603473776003603509856004603545978-3-031-42791-6DE-He21320251030112606.0cr nn 008mamaa240701s2024    sz |    s    |||| 0|eng d  a97830314279167 a10.1007/978-3-031-42791-62doi 4aQA273.A1-274.9 7aPBT2bicssc 7aPBWL2bicssc 7aMAT0290002bisacsh 7aPBT2thema 7aPBWL2thema1 aGovindan, T. E.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aTrotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applicationsh[electronic resource] /cby T. E. Govindan.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aXIX, 311 p. 1 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 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.  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. 0aProbabilities. 0aMathematical analysis. 0aSystem theory. 0aControl theory.14aProbability Theory.24aAnalysis.24aSystems Theory, Control.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303142790908iPrinted edition:z978303142792308iPrinted edition:z978303142793040uhttps://doi.org/10.1007/978-3-031-42791-6