Liu, Wei: Fine properties of stochastic evolution equations and their applications. 2009
Inhalt
- Introduction
- 1 Preliminaries on Stochastic Analysis in Infinite Dimensional Space
- 1.1 Stochastic integral in Hilbert space
- 1.1.1 Infinite dimensional Wiener processes
- 1.1.2 Martingales in Banach space
- 1.1.3 Stochastic integral in Hilbert space
- 1.2 Variational approach for stochastic evolution equations
- 1.3 Different concepts of solution to stochastic equations
- 2 Freidlin-Wentzell Large Deviations for Stochastic Evolution Equations
- 2.1 Introduction to weak convergence approach
- 2.2 Freidlin-Wentzell large deviation principle: the main results
- 2.3 Proof of the large deviation principle
- 2.4 Applications to different types of SPDE
- 3 Harnack Inequality and Its Applications to SEE
- 3.1 Introduction to Harnack inequality
- 3.2 Review on the strong Feller property and uniqueness of invariant measures
- 3.3 Harnack inequality and its applications: the main results
- 3.4 Applications to SPDE with strongly dissipative drifts
- 4 Harnack Inequality for Stochastic Fast Diffusion Equations
- 4.1 The main results on Harnack inequality
- 4.2 Proof of the Harnack inequality
- 4.3 Applications to explicit examples
- 5 Ergodicity for Stochastic p-Laplace Equation
- 5.1 Introduction and the main results
- 5.2 Applications to stochastic p-Laplace equation and reaction-diffusion equations
- 6 Invariance of Subspaces under The Solution Flow of SPDE
- Bibliography