Weak convergence to the law of the brownian sheet

Key words: frational Brownian motion, Gaussian proesses, H older regu-.. larity, loal asymptoti self-similarity,

The almost sure sample function behavior of the vector-valued fractional Brownian sheet is investigated.. In particular, the global and the local moduli of continuity of the

In the second section almost sure convergence of the generalized quadratic variations is established, a Central Limit Theorem is also obtained.. Section 3 is devoted to the

The maximal inequality (1.1) also implies a capacity estimate in Wiener space (Corollary 4.2), as well as a uniform ratio ergodic theorem for Brownian motion in Wiener space that

A process whose k-dimensional marginals coincide with those of Brownian motion will be called a weak Brownian motion of order2. In Section 4, this characterization will

We prove functional central and non-central limit theorems for generalized varia- tions of the anisotropic d-parameter fractional Brownian sheet (fBs) for any natural number d..

In this paper we use Malliavin calculus and multiple stochastic integrals to study the asymp- totic behavior of the non-weighted (i.e. f ≡ 1) Hermite variations, where the fBm

The linear Boltzmann equation has been derived (globally in time) from the dynamics of a tagged particle in a low density Lorentz gas, meaning that.. • the obstacles are