Luca M. Giordano, Maria Jolis, Lluís Quer-Sardanyons
Published 2018-10-08Version 1
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.
From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the Lévy area of fractional Brownian motion with Hurst index $α\in(1/8,1/4)$
Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion
A note on the continuity in the Hurst index of the solution of rough differential equations driven by a fractional Brownian motion
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