The recently developed theory of wavelets is used to estimate small ball probability for a class of Gaussian processes including d-dimensional fractional Brownian motion.

The paper obtains the general form of the cross-covariance function of vector fractional Brownian motion with correlated components having different self-similarity indices.

We prove a change of variable formula for the 2D fractional Brownian motion of index H bigger or equal to 1/4. For H strictly bigger than 1/4, our formula coincides with that obtained by using the rough paths theory. For H = 1/4 (the more interesting case), there is an additional term that is a classical Wiener integral against an independent standard Brownian motion.

By using Malliavin calculus and multiple Wiener-Itô integrals, we study the existence and the regularity of stochastic currents defined as Skorohod (divergence) integrals with respect to the Brownian motion and to the fractional Brownian motion. We consider also the multidimensional multiparameter case and we compare the regularity of the current as a distribution in negative Sobolev spaces wit...

Abstract. We study a class of mean-field stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈ (1/2, 1) and a related stochastic control problem. We derive a Pontryagin type maximum principle and the associated adjoint mean-field backward stochastic differential equation driven by a classical Brownian motion, and we prove that under certain assumption...

We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a timedependent kernel with respect to a standard Brownian motion. For these processes which are natural generalization of fractional Brownian motion, we construct a stochastic integral and show some of its main properties: regularity with respect to ...

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

Applying an upper bound estimate for small L2 ball probability for fractional Brownian motion (fBm), we prove the non-degeneracy of Sobolev pseudo-norms of fBm.

The CFD simulation has been undertaken concerning natural convection heat transfer of a nanofluid in vertical square enclosure, whose dimension, width height length (mm), is 40 40 90, respectively. The nanofluid used in the present study is -water with various volumetric fractions of the alumina nanoparticles ranging from 0-3%. The Rayleigh number is . Fluent v6.3 is used to simulate nanofluid ...