03928nam 2200577 a 450 991046281160332120200520144314.0981-4452-36-X(CKB)2670000000372491(EBL)1223953(OCoLC)854974290(SSID)ssj0001149807(PQKBManifestationID)11608570(PQKBTitleCode)TC0001149807(PQKBWorkID)11173744(PQKB)11422037(MiAaPQ)EBC1223953(WSP)00003065(PPN)182197514(Au-PeEL)EBL1223953(CaPaEBR)ebr10719550(CaONFJC)MIL496434(EXLCZ)99267000000037249120130622d2013 uy 0engur|n|---|||||txtccrThree classes of nonlinear stochastic partial differential equations[electronic resource] /Jie XiongSingapore World Scientific Pub. Co.20131 online resource (177 p.)Description based upon print version of record.981-4452-35-1 Includes bibliographical references and index.Preface; 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 Introduction4.2 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 definitions7.2 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; IndexThe 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 toStochastic partial differential equationsElectronic books.Stochastic partial differential equations.515.353Xiong Jie736517MiAaPQMiAaPQMiAaPQBOOK9910462811603321Three classes of nonlinear stochastic partial differential equations2237298UNINA