Three classes of nonlinear stochastic partial differential equations
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 t...
| Autor principal: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
[Hackensack] New Jersey :
World Scientific
[2013]
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| Colección: | EBSCO Academic eBook Collection Complete.
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| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b30841781*spi |
Tabla de Contenidos:
- 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.
