In a previous paper, we studied the ergodic properties of an Euler scheme of a stochastic differential equation with a Gaussian additive noise in order to approximate the stationary regime of such an equation. We now consider the case of multiplicative noise when the Gaussian process is a...

We establish large deviation estimates for the optimal filter where the observation process is corrupted by a fractional Brownian motion. The observation process is transformed to an equivalent model which is driven by a standard Brownian motion. The large deviations in turn are established by...

We prove a central limit theorem for functionals of two independent d-dimensional fractional Brownian motions with the same Hurst index H in (2d+2,2d) using the method of moments.

A unified asymptotic theory for nearly unstable higher order autoregressive processes and their least squares estimates is established. A novel version of Jordan’s canonical decomposition with perturbations together with a suitable plug-in principle is proposed to develop the underlying...

We give both necessary and sufficient conditions for a random variable to be represented as a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand. We also show that any random variable is a value of such integral in an improper sense and that such...

We construct fractional Brownian motion, sub-fractional Brownian motion and negative sub-fractional Brownian motion by means of limiting procedures applied to some particle systems. These processes are obtained for full ranges of Hurst parameter.

We consider a stochastic differential equation involving a pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed values of the solution. The rate of convergence of...

For a Gaussian process X and smooth function f, we consider a Stratonovich integral of f(X), defined as the weak limit, if it exists, of a sequence of Riemann sums. We give covariance conditions on X such that the sequence converges in law. This gives a change-of-variable formula in law with a...

We study a fractional stochastic perturbation of a first-order hyperbolic equation of nonlinear type. The existence and uniqueness of the solution are investigated via a Lax–Oleĭnik formula. To construct the invariant measure we use two main ingredients. The first one is the notion of a...

In this paper we discuss existence and uniqueness results for BSDEs driven by centered Gaussian processes. Compared to the existing literature on Gaussian BSDEs, which mainly treats fractional Brownian motion with Hurst parameter H1/2, our main contributions are: (i) Our results cover a wide...