Semi-discrete semi-linear parabolic SPDEs

DOI10.1214/14-AAP1065zbMath1325.60108arXiv1311.2199MaRDI QIDQ748326

Nicos Georgiou, Shang-Yuan Shiu, Davar Khoshnevisan, Mathew Joseph

Publication date: 20 October 2015

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.2199

zbMATH Keywords

comparison principleLyapunov exponentsparabolic Anderson modeldissipative behaviorinteracting Itō diffusionssemi-discrete stochastic heat equationsemi-linear parabolic stochastic partial differential equations

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random operators and equations (aspects of stochastic analysis) (60H25) Diffusion processes (60J60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Processes in random environments (60K37) Random linear operators (47B80)

Related Items (3)

An approximation result for a class of stochastic heat equations with colored noise ⋮ Weak intermittency of stochastic heat equation under discretizations ⋮ Intermittence and space-time fractional stochastic partial differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Regularity of the density for the stochastic heat equation
• Intermittence and nonlinear parabolic stochastic partial differential equations
• An infinite dimensional stochastic differential equation with state space C(\({\mathbb{R}})\)
• Infinite dimensional stochastic differential equations and their applications
• On the \(L^p\) norms of stochastic integrals and other martingales
• Ergodic theorems for infinite systems of locally interacting diffusions
• Comparison theorems for stochastic differential equations in finite and infinite dimensions
• The stochastic heat equation: Feynman-Kac formula and intermittence.
• Comparison of interacting diffusions and an application to their ergodic theory
• Ergodic theorems and exponential decay of sample paths for certain interacting diffusion systems
• A concise course on stochastic partial differential equations
• Quenched to annealed transition in the parabolic Anderson problem
• Phase transitions for the long-time behavior of interacting diffusions
• On large deviations for the parabolic Anderson model
• Moments and Lyapunov exponents for the parabolic Anderson model
• Extrapolation and interpolation of quasi-linear operators on martingales
• L\({}^ p\) estimates on iterated stochastic integrals
• Asymptotics for the almost sure lyapunov exponent for the solution of the parabolic Anderson problem
• Fluctuation exponent of the KPZ/stochastic Burgers equation
• Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
• Random motion of strings and related stochastic evolution equations
• On the support of solutions to the heat equation with noise
• Martingale Transforms
• Parabolic Anderson problem and intermittency
• Local Behaviour of Solutions of Stochastic Integral Equations

This page was built for publication: Semi-discrete semi-linear parabolic SPDEs