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.

In this paper, by using a Taylor development type formula, we show how it is possible to associate differential operators with stochastic differential equations driven by a fractional Brownian motion. As an application, we deduce that invariant measures for such SDEs must satisfy an infinite dimensional system of partial differential equations.

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

Let {I?. (t), 0 < t < I} be a fractional Brownian motion of order-I t: (0. 2). and let f?(t) = 13, (t) be the standard Brownian motion. We show the existence of a t'. E (0.x) such that: where u-, is an explicit constant and 8 AcadCmie des Sciences/Elsevier. Paris L'existence de la &mite pour l'asymptotique des petites boules du mouvement brourtien fractionnaire

In this paper the whole family of fractional Brownian motions is constructed as a single Gaussian field indexed by time and the Hurst index simultaneously. The field has a simple covariance structure and it is related to two generalizations of fractional Brownian motion known as multifractional Brownian motions. A mistake common to the existing literature regarding multifractional Brownian moti...

We penalise Brownian motion by a function of its one-sided supremum considered up to the last zero before t, resp. first zero after t, of that Brownian motion. This study presents some analogy with penalisation by the longest length of Brownian excursions, up to time t.

Abstract. We consider a super-Brownian motion X. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting behavior of the volume of the ε-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous result for the range of super-Brownian motion and for the support of the integrated super-Brownian ex...

In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka’s formula for linear Brownian motion. The paper is closed with a description of the boun...

Let B = {Bα(t), t ∈ RN} be an (N, d)-fractional Brownian motion with Hurst index α ∈ (0, 1). By applying the strong local nondeterminism of B, we prove certain forms of uniform Hausdorff dimension results for the images of B when N > αd. Our results extend those of Kaufman [7] for one-dimensional Brownian motion. Running head: Dimensional Properties of Fractional Brownian Motion 2000 AMS Classi...

We consider Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. We prove a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index H [ 2 . For the case H> 2 we show that such a representation cannot hold. We also consider briefly the connection between Hitsuda and Girsanov representations. Using the...