03953nam 22006495 450 991030011140332120250609112051.03-319-94893-810.1007/978-3-319-94893-5(CKB)4100000006999495(MiAaPQ)EBC5540871(DE-He213)978-3-319-94893-5(PPN)231458312(MiAaPQ)EBC6235604(EXLCZ)99410000000699949520181003d2018 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierStochastic Evolution Systems Linear Theory and Applications to Non-Linear Filtering /by Boris L. Rozovsky, Sergey V. Lototsky2nd ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (340 pages)Probability Theory and Stochastic Modelling,2199-3130 ;893-319-94892-X 1 Examples and Auxiliary Results -- 2 Stochastic Integration in a Hilbert Space -- 3 Linear Stochastic Evolution Systems in Hilbert Spaces -- 4 Ito's Second Order Parabolic Equations -- 5 Ito's Partial Differential Equations and Diffusion Processes -- 6 Filtering, Interpolation and Extrapolation of Diffusion Processes -- 7 Hypoellipticity of Ito's Second Order Parabolic Equations -- 8 Chaos Expansion for Linear Stochastic Evolution Systems -- Notes -- References -- Index.This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.Probability Theory and Stochastic Modelling,2199-3130 ;89ProbabilitiesDifferential equations, PartialFunctional analysisElectrical engineeringMathematical physicsProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Electrical Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/T24000Theoretical, Mathematical and Computational Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19005Probabilities.Differential equations, Partial.Functional analysis.Electrical engineering.Mathematical physics.Probability Theory and Stochastic Processes.Partial Differential Equations.Functional Analysis.Electrical Engineering.Theoretical, Mathematical and Computational Physics.519.22Rozovsky Boris Lauthttp://id.loc.gov/vocabulary/relators/aut767827Lototsky Sergey V.authttp://id.loc.gov/vocabulary/relators/autBOOK9910300111403321Stochastic Evolution Systems2053521UNINA