We establish diffusion and fractional Brownian motion approximations for motions in a Markovian Gaussian random field with a nonzero mean.

We derive a series expansion for the multiparameter fractional Brownian motion. The derived expansion is proven to be rate optimal .

We study simple approximations to fractional Gaussian noise and fractional Brownian motion. The approximations are based on spectral properties of the noise. They allow one to consider the noise as the result of fractional integration/differentiation of a white Gaussian noise. We study correlation properties of the approximation to fractional Gaussian noise and point to the peculiarities of per...

Fractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces and discuss a few applications. First we show q-variation regularity of Cameron-Martin paths associated to fractional Brownian motion and other Volterra processes. This is useful, for instance, to establis...

We investigate the asymptotic properties of the sequential maximum likelihhod estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process satisfying a linear stochastic differential equation driven by fractional Brownian motion.

We approximate the solution of a quasilinear stochastic partial differential equation driven by fractional Brownian motion BH(t); H ∈ (0, 1), which was calculated via fractional White Noise calculus, see [5].

We prove limit theorems for the weighted quadratic variation of trifractional Brownian motion and n-th order fractional motion. Furthermore, a sufficient condition LP-convergence Gaussian processes is obtained as byproduct. As an application, we give statistical estimator self-similarity index These extend results Baxter, Gladyshev, Norvaisa.