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050 00 a| QA274.25b| .X57 2013;

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100 1 a| Xiong, Jie.=| ^A1201131;

245 10 a| Three classes of nonlinear stochastic partial differential equationsh| [electronic resource] /c| Jie Xiong, University of Macau, China & The University of Tennessee, Knoxville, USA.;

260 a| [Hackensack,] New Jersey :b| World Scientific,c| [2013];

300 a| xi, 164 pages ;c| 24 cm;

504 a| Includes bibliographical references (pages 157-162) and index.;

505 0 a| 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. 4.2. Solution for the system. 4.3. 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. 7.2. Itô-Pardoux-Peng formula. 7.3. 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.;

506 a| Available only to authorized users.;

520 a| The 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 these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs.--c| Source other than Library of Congress;

538 a| Mode of access: World Wide Web;

650 0 a| Stochastic partial differential equations.=| ^A269969;

650 0 a| Differential equations, Nonlinear.=| ^A17363;

650 7 a| Differential equations, Nonlinear.2| fast;

650 7 a| Stochastic partial differential equations.2| fast;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=1223953;

947 a| (OCoLC)ocn823897015;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 4302688-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/4/2016x| EBOOKz| JERESOURCE;

Three classes of nonlinear stochastic partial differential equations / Jie Xiong, University of Macau, China & The University of Tennessee, Knoxville, USA.

Author/creator	Xiong, Jie
Format	Electronic
Publication Info	[Hackensack,] New Jersey : World Scientific, [2013]
Description	xi, 164 pages ; 24 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Stochastic partial differential equations. Differential equations, Nonlinear.

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. 4.2. Solution for the system. 4.3. 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. 7.2. Itô-Pardoux-Peng formula. 7.3. 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.
Abstract	The 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 these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs.-- Source other than Library of Congress
Bibliography note	Includes bibliographical references (pages 157-162) and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2013444905
ISBN	9814452351
ISBN	9789814452359

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Three classes of nonlinear stochastic partial differential equations / Jie Xiong, University of Macau, China & The University of Tennessee, Knoxville, USA.

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