Details
| Title | Stochastic PDEs and Dynamics |
|---|---|
| Creators | Guo Boling. |
| Imprint | De Gruyter, 2016 |
| Collection | Электронные книги зарубежных издательств ; Общая коллекция |
| Subjects | Stochastic partial differential equations. ; Dynamics. ; MATHEMATICS / Applied ; MATHEMATICS / Probability & Statistics / General ; EBSCO eBooks |
| Document type | Other |
| File type | |
| Language | English |
| Rights | Доступ по паролю из сети Интернет (чтение, печать, копирование) |
| Record key | ocn965135054 |
| Record create date | 12/2/2016 |
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- Preface
- Contents
- 1 Preliminaries
- 1.1 Preliminaries in probability
- 1.1.1 Probability space
- 1.1.2 Random variable and probability distribution
- 1.1.3 Mathematical expectation and momentum
- 1.2 Some preliminaries of stochastic process
- 1.2.1 Markov process
- 1.2.2 Preliminaries on ergodic theory
- 1.3 Martingale
- 1.4 Wiener process and Brown motion
- 1.5 Poisson process
- 1.6 Lévy process
- 1.6.1 Characteristic function and infinite divisibility
- 1.6.2 Lévy process
- 1.6.3 Lévy–Itô decomposition
- 1.7 The fractional Brownian motion
- 1.1 Preliminaries in probability
- 2 The stochastic integral and Itô formula
- 2.1 Stochastic integral
- 2.1.1 Itô integral
- 2.1.2 The stochastic integral in general case
- 2.1.3 Poisson stochastic integral
- 2.2 Itô formula
- 2.3 The infinite-dimensional case
- 2.3.1 Q-Wiener process and the stochastic integral
- 2.3.2 Itô formula
- 2.4 Nuclear operator and HS operator
- 2.1 Stochastic integral
- 3 OU processes and SDEs
- 3.1 Ornstein–Uhlenbeck processes
- 3.2 Linear SDEs
- 3.3 Nonlinear SDEs
- 4 Random attractors
- 4.1 Determinate nonautonomous systems
- 4.2 Stochastic dynamical systems
- 5 Applications
- 5.1 Stochastic GL equation
- 5.1.1 The existence of random attractor
- 5.1.2 Hausdorff dimension of random attractor
- 5.1.3 Generalized SGLE
- 5.2 Ergodicity for SGL with degenerate noise
- 5.2.1 Momentum estimate and pathwise uniqueness
- 5.2.2 Invariant measures
- 5.2.3 Ergodicity
- 5.2.4 Some remarks
- 5.3 Stochastic damped forced Ostrovsky equation
- 5.3.1 Introduction
- 5.3.2 Well-posedness
- 5.3.3 Uniform estimates of solutions
- 5.3.4 Asymptotic compactness and random attractors
- 5.4 Simplified quasi-geostrophic model
- 5.4.1 The existence and uniqueness of solution
- 5.4.2 Existence of random attractors
- 5.5 Stochastic primitive equations
- 5.5.1 Stochastic 2D primitive equations with Lévy noise
- 5.5.2 Large deviation for stochastic primitive equations
- 5.1 Stochastic GL equation
- Bibliography
- Index
