• Corpus ID: 238531692

On Besov regularity and local time of the stochastic heat equation

@inproceedings{Boufoussi2020OnBR,
  title={On Besov regularity and local time of the stochastic heat equation},
  author={Brahim Boufoussi and Yassine Nachit},
  year={2020}
}
Sharp Besov regularities in time and space variables are investigated for (u(t, x), t ∈ [0, T ], x ∈ R), the mild solution to the stochastic heat equation driven by space-time white noise. Existence, Hölder continuity, and Besov regularity of local times are established for u(t, x) viewed either as a process in the space variable or time variable. Hausdorff dimensions of their corresponding level sets are also obtained. 
View PDF on arXiv

60 References

Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains

We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential…

On temporal regularity of stochastic convolutions in $2$-smooth Banach spaces

  • M. OndrejátM. Veraar
  • Mathematics
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
  • 2020
We show that paths of solutions to parabolic stochastic differential equations have the same regularity in time as the Wiener process (as of the current state of art). The temporal regularity is…

Sample paths of the solution to the fractional-colored stochastic heat equation

Let {u(t,x),t ∈ [0,T],x ∈ ℝd} be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the…

Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise

Abstract In this article, we study the following stochastic heat equation where is the generator of a Lévy process X in B is a fractional-colored Gaussian noise with Hurst index in the time variable…

Initial measures for the stochastic heat equation

We consider a family of nonlinear stochastic heat equations of the form @tu = Lu + (u) _ W , where _ W denotes space-time white noise, L the generator of a symmetric L evy process on R, and is…

The Stochastic Heat Equation with a Fractional-Colored Noise: Existence of the Solution

In this article we consider the stochastic heat equation ut −�u = u B in (0,T) ×R d , with vanishing initial conditions, driven by a Gaussian noise u B which is fractional in time, with Hurst index H…

Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions

We study the nonlinear stochastic heat equation in the spatial domain R, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be…

Regularity of the sample paths of a class of second-order SPDE"s

Besov Regularity of Stochastic Partial Differential Equations on Bounded Lipschitz Domains

Spatial Besov regularity of SPDEs An Lp-theory for SPDEs on bounded Lipschitz domains [5] Let p ∈ [2,∞) and θ ≈ d + p− 2. Assume that f ∈ Lp(ΩT ;H γ−2 p,θ+p(O)) & (g k) ∈ Lp(ΩT ;H γ−1 p,θ (O; l2)) &…

A Kolmogorov and Tightness Criterion in Modular Besov Spaces and an Application to a Class of Gaussian Processes

Abstract The purpose of this paper is to prove a Kolmogorov and a tightness criterion in a class of modular Besov spaces that present a natural extension of the work in [8]. We apply these criteria…
...