Initial measures for the stochastic heat equation

DOI10.1214/12-AIHP505zbMath1288.60077arXiv1110.4079MaRDI QIDQ2438258

Davar Khoshnevisan, Shang-Yuan Shiu, Mathew Joseph, Daniel Conus

Publication date: 10 March 2014

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.4079

zbMATH Keywords

stochastic heat equationsingular initial data

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (13)

Chaotic characterization of one dimensional stochastic fractional heat equation ⋮ Some recent progress on stochastic heat equations ⋮ Stochastic heat equation: numerical positivity and almost surely exponential stability ⋮ On Besov regularity and local time of the solution to the stochastic heat equation ⋮ Continuity and strict positivity of the multi-layer extension of the stochastic heat equation ⋮ Nonlinear stochastic time-fractional diffusion equations on $\mathbb {R}$: Moments, Hölder regularity and intermittency ⋮ Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions ⋮ Polynomial chaos and scaling limits of disordered systems ⋮ Nonlinear stochastic time-fractional slow and fast diffusion equations on \(\mathbb{R}^d\) ⋮ Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions ⋮ Moments, intermittency and growth indices for the nonlinear fractional stochastic heat equation ⋮ Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial condition ⋮ Spatial asymptotics for the Feynman-Kac formulas driven by time-dependent and space-fractional rough Gaussian fields with the measure-valued initial data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the chaotic character of the stochastic heat equation, before the onset of intermitttency
• On the global maximum of the solution to a stochastic heat equation with compact-support initial data
• Intermittence and nonlinear parabolic stochastic partial differential equations
• 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 heat equation: Feynman-Kac formula and intermittence.
• On the stochastic Burgers' equation in the real line
• Some non-linear s. p. d. e's that are second order in time
• Weak nonmild solutions to some SPDEs
• Extrapolation and interpolation of quasi-linear operators on martingales
• L\({}^ p\) estimates on iterated stochastic integrals
• A local-time correspondence for stochastic partial differential equations
• Dynamic Scaling of Growing Interfaces
• On the support of solutions to the heat equation with noise
• Martingale Transforms
• Parabolic Anderson problem and intermittency

This page was built for publication: Initial measures for the stochastic heat equation