281 citations
- University of LeicesterGB34 papers
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4 papers · 1 filter
Wiener integrals with respect to the Hermite random field and applications to the wave equation
Jorge Clarke de La Cerda, Ciprian A. Tudor
The Hermite random field has been introduced as a limit of some weighted Hermite variations of the fractional Brownian sheet. In this work we define it as a multiple integral with…
The density of the solution to the stochastic transport equation with fractional noise
Christian Olivera, Ciprian Tudor
We consider the transport equation driven by the fractional Brownian motion. We study the existence and the uniqueness of the weak solution and, by using the tools of the Malliavin…
Asymptotic behavior of the quadratic variation of the sum of two Hermite processes of consecutive orders
Marianne Clausel, François Roueff, Murad Taqqu +1
Hermite processes are self--similar processes with stationary increments which appear as limits of normalized sums of random variables with long range dependence. The Hermite proce…
Homogenization of a singular random one-dimensional PDE
Bogdan Iftimie, Étienne Pardoux, Andrey Piatnitski
This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show…