SPDEs with affine multiplicative fractional noise in space with index 1/4 < H < 1/2

被引：29

作者：

Balan, Raluca M. ^{[1
]}

Jolis, Maria ^{[2
]}

Quer-Sardanyons, Lluis ^{[2
]}

机构：

[1] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2015年 / 20卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

stochastic wave equation; stochastic heat equation; fractional Brownian motion; random field solution; STOCHASTIC WAVE-EQUATION; HEAT-EQUATION; DRIVEN; SMOOTHNESS; DENSITY; FORMULA;

D O I：

10.1214/EJP.v20-3719

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this article, we consider the stochastic wave and heat equations on R with non-vanishing initial conditions, driven by a Gaussian noise which is white in time and behaves in space like a fractional Brownian motion of index H, with 1/4 < H < 1/2. We assume that the diffusion coefficient is given by an affine function sigma(x) = ax + b, and the initial value functions are bounded and Holder continuous of order H. We prove the existence and uniqueness of the mild solution for both equations. We show that the solution is L-2 (Omega) -continuous and its p-th moments are uniformly bounded, for any p >= 2

引用

页码：1 / 36

页数：36

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SPDEs with affine multiplicative fractional noise in space with index 1/4 &lt; H &lt; 1/2

SPDEs with affine multiplicative fractional noise in space with index 1/4 < H < 1/2