A concise course on stochastic partial differential equations

DOI10.1007/978-3-540-70781-3zbMath1123.60001OpenAlexW609699901MaRDI QIDQ2369708

Claudia Prévôt, Michael Roeckner

Publication date: 19 June 2007

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-70781-3

zbMATH Keywords

textbookstochastic partial differential equationsinvariant measureItô formulavariational solutionsweak monotonicity

Mathematics Subject Classification ID

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory (60-01) PDEs with randomness, stochastic partial differential equations (35R60) Stochastic analysis (60Hxx)

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noise with increasing Lipschitz nonlinearities, Stochastic Burgers type equations with reflection: existence, uniqueness, Variational solutions to nonlinear stochastic differential equations in Hilbert spaces, The Neumann problem for a Barenblatt equation with a multiplicative stochastic force and a nonlinear source term, On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations, Adaptive concepts for stochastic partial differential equations, Weak pullback attractors for stochastic Ginzburg-Landau equations in Bochner spaces, Rigorous mean-field limit and cross-diffusion, A new approach to the existence of invariant measures for Markovian semigroups, Finite-time singularity of the stochastic harmonic map flow, Stochastic heat equations with logarithmic nonlinearity, Solution to a stochastic 3D nonlocal Cahn-Hilliard-Navier-Stokes model with shear dependent viscosity via a splitting-up method, Porous media equations with multiplicative space-time white noise, Noise effect in a stochastic generalized Camassa-Holm equation, Quasi-linear SPDEs in divergence form, Real-time estimation and prediction of unsteady flows using reduced-order models coupled with few measurements, Finite element methods and their error analysis for SPDEs driven by Gaussian and non-Gaussian noises, A modified semi-implicit Euler-Maruyama scheme for finite element discretization of SPDEs with additive noise, Weak pullback attractors for mean random dynamical systems in Bochner spaces, Diffusion limit for the random walk Metropolis algorithm out of stationarity, Supremum estimates for degenerate, quasilinear stochastic partial differential equations, A note on stochastic semilinear equations and their associated Fokker-Planck equations, \(L^p\)-strong solutions of stochastic partial differential equations with monotonic drifts, Loss of regularity for Kolmogorov equations, Finite-dimensional representations for controlled diffusions with delay, On the existence of the dual right Markov process and applications, A stochastic heat equation with nonlinear dissipation on the boundary, A Milstein scheme for SPDEs, Sub and supercritical stochastic quasi-geostrophic equation, Convergence analysis of multilevel Monte Carlo variance estimators and application for random obstacle problems, An approximation scheme for reflected stochastic differential equations with non-Lipschitzian coefficients, Stochastic Navier-Stokes equations in unbounded channel domains, Wasserstein-based methods for convergence complexity analysis of MCMC with applications, Existence and regularity results for stochastic fractional pseudo-parabolic equations driven by white noise