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arXiv · 1911.12264

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

Luca M. Giordano·Maria Jolis·Lluís Quer-Sardanyons
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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 $H\in (\frac 14,1)$. 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.

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Luca M. Giordano, Maria Jolis, Lluís Quer-Sardanyons. 2019-11-27. SPDEs with linear multiplicative fractional noise: continuity in law with respect to the Hurst index. https://arxiv.org/abs/1911.12264

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