Spatial ergodicity for SPDEs via Poincaré-type inequalities
From MaRDI portal
Publication:2076619
DOI10.1214/21-EJP690zbMath1483.60091arXiv1907.11553OpenAlexW4206507248MaRDI QIDQ2076619
Le Chen, David Nualart, Fei Pu, Davar Khoshnevisan
Publication date: 22 February 2022
Published in: Electronic Journal of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1907.11553
Stationary stochastic processes (60G10) Ergodicity, mixing, rates of mixing (37A25) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)
Related Items
Another look at the Balázs-Quastel-Seppäläinen theorem ⋮ Convergence of densities of spatial averages of stochastic heat equation ⋮ Central limit theorems for stochastic wave equations in dimensions one and two ⋮ Fluctuation exponents of the KPZ equation on a large torus ⋮ The law of the iterated logarithm for spatial averages of the stochastic heat equation ⋮ Almost sure central limit theorems for stochastic wave equations ⋮ An almost sure central limit theorem for the parabolic Anderson model with delta initial condition ⋮ The stochastic heat equation with multiplicative Lévy noise: existence, moments, and intermittency ⋮ Macroscopic multi-fractality of Gaussian random fields and linear stochastic partial differential equations with colored noise ⋮ Feynman-Kac formula for iterated derivatives of the parabolic Anderson model ⋮ Unnamed Item ⋮ Gaussian fluctuation for spatial average of parabolic Anderson model with Neumann/Dirichlet/periodic boundary conditions
Uses Software
Cites Work
- Spatial asymptotics for the parabolic Anderson models with generalized time-space Gaussian noise
- On the chaotic character of the stochastic heat equation. II
- On the chaotic character of the stochastic heat equation, before the onset of intermitttency
- Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs
- Two-point correlation function and Feynman-Kac formula for the stochastic heat equation
- Intermittency and multifractality: a case study via parabolic stochastic PDEs
- Stochastic heat equation with rough dependence in space
- Intermittence and nonlinear parabolic stochastic partial differential equations
- L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel
- On the \(L^p\) norms of stochastic integrals and other martingales
- Extending martingale measure stochastic integral with applications to spatially homogeneous S. P. D. E's
- The stochastic wave equation in two spatial dimensions
- Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
- Nonlinear stochastic wave and heat equations
- The stochastic heat equation: Feynman-Kac formula and intermittence.
- A macroscopic multifractal analysis of parabolic stochastic PDEs
- Large time asymptotics for the parabolic Anderson model driven by space and time correlated noise
- A stochastic wave equation in two space dimensions: smoothness of the law
- On strongly Petrovskiĭ's parabolic SPDEs in arbitrary dimension and application to the stochastic Cahn-Hilliard equation
- Gaussian fluctuations for the stochastic heat equation with colored noise
- A central limit theorem for the stochastic heat equation
- The Cauchy problem for a nonlinear stochastic wave equation in any dimension
- Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise
- Comparison principle for stochastic heat equation on \(\mathbb{R}^{d}\)
- On the existence and position of the farthest peaks of a family of stochastic heat and wave equations
- Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
- Extrapolation and interpolation of quasi-linear operators on martingales
- L\({}^ p\) estimates on iterated stochastic integrals
- Malliavin's calculus and stochastic integral representations of functional of diffusion processes†
- The Malliavin Calculus and Related Topics
- On the support of solutions to the heat equation with noise
- [https://portal.mardi4nfdi.de/wiki/Publication:4060205 Repr�sentation de martingales vectorielles de carr� int�grable � valeurs dans des espaces de Hilbert r�els s�parables]
- Martingale Transforms
- Potential Theory of Lévy Processes
- Parabolic Anderson problem and intermittency
- Multiparameter Processes
- On the stochastic heat equation with spatially-colored random forcing
- Stopping Times and Directed Processes
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item