Add to ORKGThis 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 1/4<H<1/2 in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient is differentiable with a Lipschitz derivative and vanishes at 0. In the case of a multiplicative noise, that is the linear equation, we derive the Wiener chaos expansion of the solution and a Feynman-Kac formula for the moments of the solution. These results allow us to establish sharp lower and upper asymptotic bounds for the moments of the solution
This paper is inspired by artides of Chow [Ch] and Nualart-Zakai [NZ], in which certain (linear) sto...
In this dissertation, we investigate some problems in fractional Brownian motion and stochastic part...
We study the propagation of high peaks (intermittency fronts) of the solution to a stochastic heat e...
This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W i...
Accessible en ligne : http://alea.impa.br/english/index_v7.htmInternational audienceIn this article ...
In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild ...
This is the published version, also available here: http://dx.doi.org/10.1214/10-AOP547.We establish...
International audienceWe consider the stochastic heat equation with multiplicative noise $u_t=\frac{...
This is the published version, also available here: http://dx.doi.org/10.1214/11-AOP649.In this pape...
We study the solutions of the stochastic heat equation driven by spatially inhomogeneous multiplicat...
In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear t...
In this paper we establish a large deviation principle for the nonlinear one dimensional stochastic...
In this paper, we establish a version of the Feynman-Kac formula for multidimensional stochastic hea...
AbstractWe consider a system of d linear stochastic heat equations driven by an additive infinite-di...
We study the law of the solution to the stochastic heat equation with additive Gaussian noise which ...
This paper is inspired by artides of Chow [Ch] and Nualart-Zakai [NZ], in which certain (linear) sto...
In this dissertation, we investigate some problems in fractional Brownian motion and stochastic part...
We study the propagation of high peaks (intermittency fronts) of the solution to a stochastic heat e...
This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W i...
Accessible en ligne : http://alea.impa.br/english/index_v7.htmInternational audienceIn this article ...
In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild ...
This is the published version, also available here: http://dx.doi.org/10.1214/10-AOP547.We establish...
International audienceWe consider the stochastic heat equation with multiplicative noise $u_t=\frac{...
This is the published version, also available here: http://dx.doi.org/10.1214/11-AOP649.In this pape...
We study the solutions of the stochastic heat equation driven by spatially inhomogeneous multiplicat...
In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear t...
In this paper we establish a large deviation principle for the nonlinear one dimensional stochastic...
In this paper, we establish a version of the Feynman-Kac formula for multidimensional stochastic hea...
AbstractWe consider a system of d linear stochastic heat equations driven by an additive infinite-di...
We study the law of the solution to the stochastic heat equation with additive Gaussian noise which ...
This paper is inspired by artides of Chow [Ch] and Nualart-Zakai [NZ], in which certain (linear) sto...
In this dissertation, we investigate some problems in fractional Brownian motion and stochastic part...
We study the propagation of high peaks (intermittency fronts) of the solution to a stochastic heat e...