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Stochastic PDEs and Dynamics.

By: Contributor(s): Material type: TextTextPublisher: Berlin/Boston : Walter de Gruyter GmbH, 2016Copyright date: ©2017Edition: 1st edDescription: 1 online resource (228 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110493887
Subject(s): Genre/Form: Additional physical formats: Print version:: Stochastic PDEs and DynamicsDDC classification:
  • 519.2/2
LOC classification:
  • QA274.25.G86 2017
Online resources:
Contents:
Intro -- 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 -- 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 -- Bibliography -- Index.
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Intro -- 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 -- 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 -- Bibliography -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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