SPDEs with fractional noise in space : Continuity in law with respect to the Hurst index

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(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Quer i Sardanyons, Lluís

(Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Fecha:	2020
Resumen:	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.
Ayudas:	Ministerio de Economía y Competitividad MTM2015-67802P
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió publicada
Materia:	Fractional noise ; Stochastic heat equation ; Stochastic wave equation ; Weak convergence
Publicado en:	Bernoulli, Vol. 26, Issue 1 (February 2020) , p. 352-386, ISSN 1350-7265

$SPDEs with fractional noise in space$

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