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 drift, we show that there is a unique solution, which has moments of all orders. We also apply the techniques of Malliavin...

We study a least squares estimator for the Ornstein-Uhlenbeck process, , driven by fractional Brownian motion BH with Hurst parameter . We prove the strong consistence of (the almost surely convergence of to the true parameter [theta]). We also obtain the rate of this convergence when 1/2=H3/4,...

In this paper we provide some sufficient conditions for the Skorohod integral process to have a continuous version. A first set of conditions require the existence of two square integrable derivatives and that the process has moments of order [beta] 2. Secondly, we prove that the existence of...

Using the Itô-Wiener chaos expansion we prove that the normalized self-intersection local time of planar Brownian motion is not differentiable in the sense of Meyer-Watanabe.

We study the problem of parameter estimation for generalized Ornstein-Uhlenbeck processes driven by [alpha]-stable noises, observed at discrete time instants. Least squares method is used to obtain an asymptotically consistent estimator. The strong consistency and the rate of convergence of the...

We prove a stochastic maximum principle for controlled processes X(t)=X(u)(t) of the formdX(t)=b(t,X(t),u(t)) dt+[sigma](t,X(t),u(t)) dB(H)(t),where B(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter . As an application we solve a problem about minimal variance hedging in...

We extend the classical Garsia–Rodemich–Rumsey inequality to the multiparameter situation. The new inequality is applied to obtain some joint Hölder continuity along the rectangles for fractional Brownian fields W(t,x) and for the solution u(t,y) of the stochastic heat equation with...