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AuthorPrato, Giuseppe Da. author
TitleKolmogorov Equations for Stochastic PDEs [electronic resource] / by Giuseppe Da Prato
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2004
Connect tohttp://dx.doi.org/10.1007/978-3-0348-7909-5
Descript VII, 182 p. online resource

CONTENT

1 Introduction and Preliminaries -- 1.1 Introduction -- 1.2 Preliminaries ix -- 2 Stochastic Perturbations of Linear Equations -- 2.1 Introduction -- 2.2 The stochastic convolution -- 2.3 The Ornsteinโ{128}{148}Uhlenbeck semigroup Rt -- 2.4 The case when Rt is strong Feller -- 2.5 Asymptotic behaviour of solutions, invariant measures -- 2.6 The transition semigroup in Lp(H, ?) -- 2.7 Poincarรฉ and log-Sobolev inequalities -- 2.8 Some complements -- 3 Stochastic Differential Equations with Lipschitz Nonlinearities -- 3.1 Introduction and setting of the problem -- 3.2 Existence, uniqueness and approximation -- 3.3 The transition semigroup -- 3.4 Invariant measure v -- 3.5 The transition semigroup in L2 (H, v) -- 3.6 The integration by parts formula and its consequences -- 3.7 Comparison of v with a Gaussian measure -- 4 Reaction-Diffusion Equations -- 4.1 Introduction and setting of the problem -- 4.2 Solution of the stochastic differential equation -- 4.3 Feller and strong Feller properties -- 4.4 Irreducibility -- 4.5 Existence of invariant measure -- 4.6 The transition semigroup in L2 (H, v) -- 4.7 The integration by parts formula and its consequences -- 4.8 Comparison of v with a Gaussian measure -- 4.9 Compactness of the embedding W1,2 (H, v) ? L2 (H, v) -- 4.10 Gradient systems -- 5 The Stochastic Burgers Equation -- 5.1 Introduction and preliminaries -- 5.2 Solution of the stochastic differential equation -- 5.3 Estimates for the solutions -- 5.4 Estimates for the derivative of the solution w.r.t. the initial datum -- 5.5 Strong Feller property and irreducibility -- 5.6 Invariant measure v -- 5.6.1 Estimate of some integral with respect to v -- 5.7 Kolmogorov equation -- 6 The Stochastic 2D Navierโ{128}{148}Stokes Equation -- 6.1 Introduction and preliminaries -- 6.2 Solution of the stochastic equation -- 6.3 Estimates for the solution -- 6.4 Invariant measure v -- 6.5 Kolmogorov equation


Mathematics Partial differential equations Probabilities Mathematics Partial Differential Equations Probability Theory and Stochastic Processes



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