## Bernoulli

• Bernoulli
• Volume 26, Number 1 (2020), 352-386.

### 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 $H\in (0,1)$. 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.

#### Article information

Source
Bernoulli, Volume 26, Number 1 (2020), 352-386.

Dates
Revised: February 2019
First available in Project Euclid: 26 November 2019

https://projecteuclid.org/euclid.bj/1574758831

Digital Object Identifier
doi:10.3150/19-BEJ1128

Mathematical Reviews number (MathSciNet)
MR4036037

Zentralblatt MATH identifier
07140502

#### Citation

Giordano, Luca M.; Jolis, Maria; Quer-Sardanyons, Lluís. SPDEs with fractional noise in space: Continuity in law with respect to the Hurst index. Bernoulli 26 (2020), no. 1, 352--386. doi:10.3150/19-BEJ1128. https://projecteuclid.org/euclid.bj/1574758831

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