Stochastic PDEs and Dynamics
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| Формат: | Электронная книга |
| Язык: | English |
| Публикация: |
De Gruyter,
2016.
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| Предметы: | |
| Online-ссылка: | EBSCOhost Перейти в каталог НБ ТГУ |
Оглавление:
- 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
- 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 ; 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