LEADER 03928nam 2200577 a 450 001 9910462811603321 005 20200520144314.0 010 $a981-4452-36-X 035 $a(CKB)2670000000372491 035 $a(EBL)1223953 035 $a(OCoLC)854974290 035 $a(SSID)ssj0001149807 035 $a(PQKBManifestationID)11608570 035 $a(PQKBTitleCode)TC0001149807 035 $a(PQKBWorkID)11173744 035 $a(PQKB)11422037 035 $a(MiAaPQ)EBC1223953 035 $a(WSP)00003065 035 $a(PPN)182197514 035 $a(Au-PeEL)EBL1223953 035 $a(CaPaEBR)ebr10719550 035 $a(CaONFJC)MIL496434 035 $a(EXLCZ)992670000000372491 100 $a20130622d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aThree classes of nonlinear stochastic partial differential equations$b[electronic resource] /$fJie Xiong 210 $aSingapore $cWorld Scientific Pub. Co.$d2013 215 $a1 online resource (177 p.) 300 $aDescription based upon print version of record. 311 $a981-4452-35-1 320 $aIncludes bibliographical references and index. 327 $aPreface; Contents; 1. Introduction to Superprocesses; 1.1 Branching particle system; 1.2 The log-Laplace equation; 1.3 The moment duality; 1.4 The SPDE for the density; 1.5 The SPDE for the distribution; 1.6 Historical remarks; 2. Superprocesses in Random Environments; 2.1 Introduction and main result; 2.2 The moment duality; 2.3 Conditional martingale problem; 2.4 Historical remarks; 3. Linear SPDE; 3.1 An equation on measure space; 3.2 A duality representation; 3.3 Two estimates; 3.4 Historical remarks; 4. Particle Representations for a Class of Nonlinear SPDEs; 4.1 Introduction 327 $a4.2 Solution for the system4.3 A nonlinear SPDE; 4.4 Historical remarks; 5. Stochastic Log-Laplace Equation; 5.1 Introduction; 5.2 Approximation and two estimates; 5.3 Existence and uniqueness; 5.4 Conditional log-Laplace transform; 5.5 Historical remarks; 6. SPDEs for Density Fields of the Superprocesses in Random Environment; 6.1 Introduction; 6.2 Derivation of SPDE; 6.3 A convolution representation; 6.4 An estimate in spatial increment; 6.5 Estimates in time increment; 6.6 Historical remarks; 7. Backward Doubly Stochastic Differential Equations; 7.1 Introduction and basic definitions 327 $a7.2 Ito-Pardoux-Peng formula7.3 Uniqueness of solution; 7.4 Historical remarks; 8. From SPDE to BSDE; 8.1 The SPDE for the distribution; 8.2 Existence of solution to SPDE; 8.3 From BSDE to SPDE; 8.4 Uniqueness for SPDE; 8.5 Historical remarks; Appendix Some Auxiliary Results; A.1 Martingale representation theorems; A.2 Weak convergence; A.3 Relation among strong existence, weak existence and pathwise uniqueness; Bibliography; Index 330 $aThe study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to 606 $aStochastic partial differential equations 608 $aElectronic books. 615 0$aStochastic partial differential equations. 676 $a515.353 700 $aXiong$b Jie$0736517 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462811603321 996 $aThree classes of nonlinear stochastic partial differential equations$92237298 997 $aUNINA