SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index

Luca M. Giordano, Maria Jolis and Lluís Quer-Sardanyons

Stochastic Processes and their Applications, 2020, vol. 130, issue 12, 7396-7430

Abstract: In this article, we consider the one-dimensional stochastic wave and heat equations driven by a linear multiplicative Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index H∈(14,1). We prove that the solution of each of the above equations is continuous in terms of the index H, with respect to the convergence in law in the space of continuous functions. The proof is based on a tightness criterion on the plane and Malliavin calculus techniques in order to identify the limit law.

Keywords: Fractional noise; Stochastic heat equation; Stochastic wave equation; Weak convergence; Wiener Chaos expansion (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2020.08.001

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