LEADER 04083nam 22006855 450 001 9910299779003321 005 20230810184115.0 010 $a3-319-12853-1 024 7 $a10.1007/978-3-319-12853-5 035 $a(CKB)3710000000311639 035 $a(EBL)1967688 035 $a(OCoLC)908087585 035 $a(SSID)ssj0001408401 035 $a(PQKBManifestationID)11891144 035 $a(PQKBTitleCode)TC0001408401 035 $a(PQKBWorkID)11347372 035 $a(PQKB)10603318 035 $a(DE-He213)978-3-319-12853-5 035 $a(MiAaPQ)EBC1967688 035 $a(PPN)183151623 035 $a(EXLCZ)993710000000311639 100 $a20141202d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic Integration in Banach Spaces $eTheory and Applications /$fby Vidyadhar Mandrekar, Barbara Rüdiger 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (213 p.) 225 1 $aProbability Theory and Stochastic Modelling,$x2199-3149 ;$v73 300 $aDescription based upon print version of record. 311 $a3-319-12852-3 320 $aIncludes bibliographical references and index. 327 $a1.Introduction -- 2.Preliminaries -- 3.Stochastic Integrals with Respect to Compensated Poisson Random Measures -- 4.Stochastic Integral Equations in Banach Spaces -- 5.Stochastic Partial Differential Equations in Hilbert Spaces -- 6.Applications -- 7.Stability Theory for Stochastic Semilinear Equations -- A Some Results on compensated Poisson random measures and stochastic integrals -- References -- Index. 330 $aConsidering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results, and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis, and in particular the theory of operator semigroups. 410 0$aProbability Theory and Stochastic Modelling,$x2199-3149 ;$v73 606 $aProbabilities 606 $aSocial sciences$xMathematics 606 $aDifferential equations 606 $aProbability Theory 606 $aMathematics in Business, Economics and Finance 606 $aDifferential Equations 615 0$aProbabilities. 615 0$aSocial sciences$xMathematics. 615 0$aDifferential equations. 615 14$aProbability Theory. 615 24$aMathematics in Business, Economics and Finance. 615 24$aDifferential Equations. 676 $a515.732 700 $aMandrekar$b Vidyadhar$4aut$4http://id.loc.gov/vocabulary/relators/aut$0142968 702 $aRüdiger$b Barbara$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299779003321 996 $aStochastic Integration in Banach Spaces$92499094 997 $aUNINA