Lp-Theory for the Stochastic Heat Equation with Infinite-Dimensional Fractional Noise
نویسنده
چکیده
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 equation has a unique solution (in a Banach space of summability exponent p ≥ 2), and this solution is Hölder continuous in both time and space.
منابع مشابه
Stochastic Heat Equation with Infinite Dimensional Fractional Noise: L2-theory
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