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6 papers · 2 filters
A singular stochastic differential equation driven by fractional Brownian motion
Yaozhong Hu, David Nualart, Xiaoming Song
In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter . Under some assumptions on the…
Central and non-central limit theorems for weighted power variations of fractional Brownian motion
Ivan Nourdin, David Nualart, Ciprian Tudor
In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q>=2 of the fractional Brownian motion with Hurst parameter…
Central limit theorems for multiple Skorohod integrals
Ivan Nourdin, David Nualart
In this paper, we prove a central limit theorem for a sequence of iterated Shorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit i…
Stochastic Heat Equation Driven by Fractional Noise and Local Time
Yaozhong Hu, David Nualart
The aim of this paper is to study the -dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractiona…
Intersection local time for two independent fractional Brownian motions
David Nualart, Salvador Ortiz-Latorre
We prove the existence of the intersection local time for two independent, d -dimensional fractional Brownian motions with the same Hurst parameter H. Assume d greater or equal to…
Existence and smoothness of the density for spatially homogeneous SPDEs
David Nualart, Lluis Quer-Sardanyons
In this paper, we extend Walsh's stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous spatial correlation, in order to be able to integrate…