TY - JOUR

T1 - SPDEs with fractional noise in space

T2 - Continuity in law with respect to the Hurst index

AU - Giordano, Luca M.

AU - Jolis, Maria

AU - Quer-Sardanyons, Lluís

N1 - 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 Economía y Competitividad).
Publisher Copyright:
© 2020 ISI/BS.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Fractional noise

KW - Stochastic heat equation

KW - Stochastic wave equation

KW - Weak convergence

UR - http://www.scopus.com/inward/record.url?scp=85076555673&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85076555673

SN - 1350-7265

VL - 26

SP - 352

EP - 386

JO - Bernoulli

JF - Bernoulli

IS - 1

ER -