LEADER 03182nam 2200625 450 001 9910674359303321 005 20231009145727.0 010 $a981-19-7670-8 024 7 $a10.1007/978-981-19-7670-4 035 $a(MiAaPQ)EBC7206795 035 $a(Au-PeEL)EBL7206795 035 $a(CKB)26186204500041 035 $a(DE-He213)978-981-19-7670-4 035 $a(PPN)268074895 035 $a(EXLCZ)9926186204500041 100 $a20230525d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSymplectic integration of stochastic Hamiltonian systems /$fJialin Hong and Liying Sun 205 $a1st ed. 2022. 210 1$aSingapore :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (307 pages) 225 1 $aLecture notes in mathematics ;$vVolume 2314 311 08$aPrint version: Hong, Jialin Symplectic Integration of Stochastic Hamiltonian Systems Singapore : Springer,c2023 9789811976698 320 $aIncludes bibliographical references. 327 $aChapter 1 Deterministic Hamiltonian System -- Chapter 2 Stochastic Hamiltonian System -- Chapter 3 Stochastic Structure Preserving Numerical Integrators -- Chapter 4 Stochastic Modified Equation and Its Applications -- Chapter 5 Stochastic Hamiltonian Partial Differential Equation. 330 $aThis book provides an accessible overview concerning the stochastic numerical methods inheriting long-time dynamical behaviours of finite and infinite-dimensional stochastic Hamiltonian systems. The long-time dynamical behaviours under study involve symplectic structure, invariants, ergodicity and invariant measure. The emphasis is placed on the systematic construction and the probabilistic superiority of stochastic symplectic methods, which preserve the geometric structure of the stochastic flow of stochastic Hamiltonian systems. The problems considered in this book are related to several fascinating research hotspots: numerical analysis, stochastic analysis, ergodic theory, stochastic ordinary and partial differential equations, and rough path theory. This book will appeal to researchers who are interested in these topics. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vVolume 2314. 606 $aHamiltonian systems 606 $aStochastic differential equations 606 $aSymplectic groups 606 $aSistemes hamiltonians$2thub 606 $aEquacions diferencials estocàstiques$2thub 606 $aGrups simplèctics$2thub 608 $aLlibres electrònics$2thub 615 0$aHamiltonian systems. 615 0$aStochastic differential equations. 615 0$aSymplectic groups. 615 7$aSistemes hamiltonians 615 7$aEquacions diferencials estocàstiques 615 7$aGrups simplèctics 676 $a514.74 700 $aHong$b Jialin$0769125 702 $aSun$b Liying 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910674359303321 996 $aSymplectic Integration of Stochastic Hamiltonian Systems$93041614 997 $aUNINA