Stochastic heat equation with rough dependence in space

Yaozhong Hu; Jingyu Huang; Khoa Le; David Nualart; Samy Tindel

doi:10.1214/16-AOP1172

Stochastic heat equation with rough dependence in space

Yaozhong Hu
, Jingyu Huang
, Khoa Le
, David Nualart
, Samy Tindel

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H∈(¼,½) in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient σ(u) is differentiable with a Lipschitz derivative and σ(0)=0.

Original language	English
Pages (from-to)	4561-4616
Number of pages	56
Journal	Annals of Probability
Volume	45
Issue number	6B
DOIs	https://doi.org/10.1214/16-AOP1172
Publication status	Published - 12 Dec 2017

Keywords

Stochastic heat equation
fractional Brownian motion
Feynman–Kac formula
Wiener chaos expansion
intermittency Citation

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Cite this

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title = "Stochastic heat equation with rough dependence in space",

abstract = "This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H∈(¼,½) in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient σ(u) is differentiable with a Lipschitz derivative and σ(0)=0.",

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AU - Hu, Yaozhong

AU - Huang, Jingyu

AU - Le, Khoa

AU - Nualart, David

AU - Tindel, Samy

PY - 2017/12/12

Y1 - 2017/12/12

N2 - This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H∈(¼,½) in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient σ(u) is differentiable with a Lipschitz derivative and σ(0)=0.

AB - This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H∈(¼,½) in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient σ(u) is differentiable with a Lipschitz derivative and σ(0)=0.

KW - Stochastic heat equation

KW - fractional Brownian motion

KW - Feynman–Kac formula

KW - Wiener chaos expansion

KW - intermittency Citation

UR - https://www.scopus.com/pages/publications/85038391911

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DO - 10.1214/16-AOP1172

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VL - 45

SP - 4561

EP - 4616

JO - Annals of Probability

JF - Annals of Probability

IS - 6B

ER -

Stochastic heat equation with rough dependence in space

Abstract

Keywords

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