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math.PR2021
A full discretization of the rough fractional linear heat equation
Aurélien Deya, Renaud Marty
We study a full discretization scheme for the stochastic linear heat equation \begin{equation*}\begin{cases}\partial_t \langleΨ\rangle = Δ\langleΨ\rangle +\dot{B}\, , \quad t\in [0…
math.PR2010★ 19 cited
A general framework for waves in random media with long-range correlations
Renaud Marty, Knut Sølna
We consider waves propagating in a randomly layered medium with long-range correlations. An example of such a medium is studied in \citeMS and leads, in particular, to an asymptoti…
math.PR2006★ 14 cited
Invariance principle, multifractional Gaussian processes and long-range dependence
Serge Cohen, Renaud Marty
This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $…