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 -