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arXiv · 1810.03692

SPDEs with fractional noise in space: 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 quasi-linear stochastic wave and heat equations on the real line and with an additive Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index $H\in (0,1)$. The drift term is assumed to be globally Lipschitz. 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.

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Luca M. Giordano, Maria Jolis, Lluís Quer-Sardanyons. 2018-10-08. SPDEs with fractional noise in space: continuity in law with respect to the Hurst index. https://arxiv.org/abs/1810.03692

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