A full discretization of the rough fractional linear heat equation

DOI10.1214/22-EJP839MaRDI QIDQ2082692

Aurélien Deya, Renaud Marty

Publication date: 4 October 2022

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.08977

zbMATH Keywords

stochastic heat equationfractional noisespace-time discretization procedure

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Heat equation (35K05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Fractional partial differential equations (35R11) Numerical analysis (65-XX)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a modelled rough heat equation
• Strong and weak approximation of semilinear stochastic evolution equations
• Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter \(H < 1/2\)
• A theory of regularity structures
• Stochastic heat equation driven by fractional noise and local time
• Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. I
• Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. II
• Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise
• Strong solutions to the stochastic quantization equations.
• Two-dimensional Navier-Stokes equations driven by a space-time white noise
• Implicit scheme for quasi-linear parabolic partial differential equations perturbed by space-time white noise
• Comparing the stochastic nonlinear wave and heat equations: a case study
• Moment estimates for some renormalized parabolic Anderson models
• On a non-linear 2D fractional wave equation
• Parabolic Anderson model with a fractional Gaussian noise that is rough in time
• Introduction to regularity structures
• Sharp mean-square regularity results for SPDEs with fractional noise and optimal convergence rates for the numerical approximations
• A nonlinear wave equation with fractional perturbation
• A multiparameter Garsia-Rodemich-Rumsey inequality and some applications
• Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
• A nonlinear Schrödinger equation with fractional noise
• Renormalization of the two-dimensional stochastic nonlinear wave equations
• Approximating Stochastic Evolution Equations with Additive White and Rough Noises
• Galerkin Finite Element Methods for Parabolic Problems
• A fully discrete approximation of the one-dimensional stochastic heat equation

This page was built for publication: A full discretization of the rough fractional linear heat equation