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Guo, Boling. Stochastic PDEs and Dynamics [[electronic resource].]: De Gruyter, 2016. — 1 online resource — <URL:http://elib.fa.ru/ebsco/1438374.pdf>.

Record create date: 12/2/2016

Subject: Stochastic partial differential equations.; Dynamics.; Dynamics.; Stochastic partial differential equations.; MATHEMATICS / Applied; MATHEMATICS / Probability & Statistics / General

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Table of Contents

  • 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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