@article{1a6a58a445134d2bab32b07881fd98bc,
title = "SPDEs with fractional noise in space: Continuity in law with respect to the Hurst index",
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 ∈ (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.",
keywords = "Fractional noise, Stochastic heat equation, Stochastic wave equation, Weak convergence",
author = "Giordano, \{Luca M.\} and Maria Jolis and Llu{\'i}s Quer-Sardanyons",
note = "Funding Information: The authors thank the anonymous referee for a careful reading of the manuscript and all comments and suggestions. Research supported by the grant MTM2015-67802P (Ministerio de Econom{\'i}a y Competitividad). Publisher Copyright: {\textcopyright} 2020 ISI/BS.",
year = "2020",
language = "English",
volume = "26",
pages = "352--386",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "Bernoulli Society for Mathematical Statistics and Probability",
number = "1",
}