Add to ORKGWe establish a version of the Feynman–Kac formula for the multidi-mensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the Feynman–Kac formula is a weak solution of the stochastic heat equation. From the Feynman–Kac formula, we establish the smooth-ness of the density of the solution and the Hölder regularity in the space and time variables. We also derive a Feynman–Kac formula for the stochastic heat equation in the Skorokhod sense and we obtain the Wiener chaos expansio
Dedicated to David Nualart on occasion of his 60th birthdayInternational audienceIn this article, we...
We give a new representation of fractional Brownian motion with Hurst parameter H ≤ 1 2 using stocha...
AbstractWe consider a system of d linear stochastic heat equations driven by an additive infinite-di...
We establish a version of the Feynman–Kac formula for the multidi-mensional stochastic heat equation...
This is the published version, also available here: http://dx.doi.org/10.1214/10-AOP547.We establish...
This is the published version, also available here: http://dx.doi.org/10.1214/11-AOP649.In this pape...
This note deals with the asymptotic behavior of a weak solution of the multidimensional stochastic h...
Abstract In this paper, we consider the stochastic heat equation of the form ∂ u ∂ t = Δ α u + ∂ 2 B...
In this dissertation, we investigate some problems in fractional Brownian motion and stochastic part...
The aim of this work is to establish and generalize a relationship between fractional partial differ...
The aim of this work is to establish and generalize a relationship between fractional partial differ...
We consider the stochastic heat equation of the form ∂u/∂t=(Δ+Δα)u+(∂f/∂x)(t,x,u)+σ(t,x,u)L˙+W˙H, wh...
We consider a system of d linear stochastic heat equations driven by an additive infinite-dimensiona...
In this article, we consider the stochastic heat equation $du=(\Delta u+f(t,x)){\rm d}t+ \sum_{k=1}^...
In this thesis, we study systems of linear and/or non-linear stochastic heat equations and fractiona...
Dedicated to David Nualart on occasion of his 60th birthdayInternational audienceIn this article, we...
We give a new representation of fractional Brownian motion with Hurst parameter H ≤ 1 2 using stocha...
AbstractWe consider a system of d linear stochastic heat equations driven by an additive infinite-di...
We establish a version of the Feynman–Kac formula for the multidi-mensional stochastic heat equation...
This is the published version, also available here: http://dx.doi.org/10.1214/10-AOP547.We establish...
This is the published version, also available here: http://dx.doi.org/10.1214/11-AOP649.In this pape...
This note deals with the asymptotic behavior of a weak solution of the multidimensional stochastic h...
Abstract In this paper, we consider the stochastic heat equation of the form ∂ u ∂ t = Δ α u + ∂ 2 B...
In this dissertation, we investigate some problems in fractional Brownian motion and stochastic part...
The aim of this work is to establish and generalize a relationship between fractional partial differ...
The aim of this work is to establish and generalize a relationship between fractional partial differ...
We consider the stochastic heat equation of the form ∂u/∂t=(Δ+Δα)u+(∂f/∂x)(t,x,u)+σ(t,x,u)L˙+W˙H, wh...
We consider a system of d linear stochastic heat equations driven by an additive infinite-dimensiona...
In this article, we consider the stochastic heat equation $du=(\Delta u+f(t,x)){\rm d}t+ \sum_{k=1}^...
In this thesis, we study systems of linear and/or non-linear stochastic heat equations and fractiona...
Dedicated to David Nualart on occasion of his 60th birthdayInternational audienceIn this article, we...
We give a new representation of fractional Brownian motion with Hurst parameter H ≤ 1 2 using stocha...
AbstractWe consider a system of d linear stochastic heat equations driven by an additive infinite-di...