Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise

Lp-Theory for the Stochastic Heat Equation with Infinite-Dimensional Fractional Noise

In this article, we consider the stochastic heat equation du = (∆u + f(t, x))dt + P∞ k=1 g(t, x)δβ t , t ∈ [0, T ], with random coefficients f and g, driven by a sequence (βk)k of i.i.d. fractional Brownian motions of index H > 1/2. Using the Malliavin calculus techniques and a p-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (βk)k, we prove that the equ...

Stochastic Heat Equation with Infinite Dimensional Fractional Noise: L2-theory

In this article we consider the stochastic heat equation in [0, T ]× Rd, driven by a sequence (β)k of i.i.d. fractional Brownian motions of index H > 1/2 and random multiplication functions (g)k. The stochastic integrals are of Hitsuda-Skorohod type and the solution is interpreted in the weak sense. Using Malliavin calculus techniques, we prove the existence and uniqueness of the solution in a ...

Stochastic Heat Equation with Multiplicative Fractional-Colored Noise

We consider the stochastic heat equation with multiplicative noise ut = 1 2 ∆u + uẆ in R+ × R , whose solution is interpreted in the mild sense. The noise Ẇ is fractional in time (with Hurst index H ≥ 1/2), and colored in space (with spatial covariance kernel f). When H > 1/2, the equation generalizes the Itô-sense equation for H = 1/2. We prove that if f is the Riesz kernel of order α, or the ...

Stochastic Heat Equation Driven by Fractional Noise and Local Time

The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (0, 1) in time. Two types of equations are considered. First we consider the equation in the Itô-Skorohod sense, and later in the Stratonovich sense. An explicit chaos developm...

Stochastic heat equation with white-noise drift