LEADER 04444nam 22005775 450 001 9910150450203321 005 20230620195220.0 010 $a3-319-45684-9 024 7 $a10.1007/978-3-319-45684-3 035 $a(CKB)3710000000943193 035 $a(DE-He213)978-3-319-45684-3 035 $a(MiAaPQ)EBC4741446 035 $a(PPN)197139507 035 $a(EXLCZ)993710000000943193 100 $a20161111d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aYosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications /$fby T. E. Govindan 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XIX, 407 p.) 225 1 $aProbability Theory and Stochastic Modelling,$x2199-3149 ;$v79 311 $a3-319-45682-2 320 $aIncludes bibliographical references and index. 327 $aPreface -- Notations and Abbreviations -- Introduction and Motivating Examples -- Mathematical machinery -- Yosida Approximations of Stochastic Differential Equations -- Yosida Approximations of Stochastic Differential Equations with Jumps -- Applications to Stochastic Stability -- Applications to Stochastic Optimal Control -- Appendix A: Nuclear and Hilbert-Schmidt Operators -- Appendix B: Multivalued Maps -- Appendix C: Maximal Monotone Operators -- Appendix D: The Duality Mapping -- Appendix E: Random Multivalued Operators -- Bibliographical Notes and Remarks -- Bibliography. 330 $aThis research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces. The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussion of the monograph, namely, Yosida approximations of SDEs, Yosida approximations of SDEs with Poisson jumps, and their applications. Most of the results considered in the main chapters appear for the first time in a book form, and contain illustrative examples on stochastic partial differential equations. The key steps are included in all proofs, especially the various estimates, which help the reader to get a true feel for the theory of Yosida approximations and their use. This work is intended for researchers and graduate students in mathematics specializing in probability theory and will appeal to numerical analysts, engineers, physicists and practitioners in finance who want to apply the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in stochastic processes. . 410 0$aProbability Theory and Stochastic Modelling,$x2199-3149 ;$v79 606 $aProbabilities 606 $aDifferential equations 606 $aControl engineering 606 $aProbability Theory 606 $aDifferential Equations 606 $aControl and Systems Theory 615 0$aProbabilities. 615 0$aDifferential equations. 615 0$aControl engineering. 615 14$aProbability Theory. 615 24$aDifferential Equations. 615 24$aControl and Systems Theory. 676 $a519.2 700 $aGovindan$b T. E$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756127 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910150450203321 996 $aYosida approximations of stochastic differential equations in infinite dimensions and applications$91523723 997 $aUNINA