Tanaka formula for the fractional Brownian motion

Brownian motion, reflection groups and Tanaka formula

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...

Ito formula for the infinite dimensional fractional Brownian motion

We introduce the stochastic integration with respect to the infinite-dimensional fractional Brownian motion. Using the techniques of the anticipating stochastic calculus, we derive an Itô formula for Hurst parameter bigger than 1 2 .

An Itô-type formula for the fractional Brownian motion in Brownian time*

Let X be a (two-sided) fractional Brownian motion of Hurst parameter H ∈ (0, 1) and let Y be a standard Brownian motion independent of X. Fractional Brownian motion in Brownian motion time (of index H), recently studied in [17], is by definition the process Z = X ◦ Y . It is a continuous, non-Gaussian process with stationary increments, which is selfsimilar of index H/2. The main result of the ...

Lacunary Fractional Brownian Motion

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Tempered fractional Brownian motion