Itô's formula for a sub-fractional Brownian motion

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 .

Ruin Probability for Generalized Φ-sub-gaussian Fractional Brownian Motion

for various types of risk process X = (X(t), t ≥ 0) and functions f(t). The similar problem of finding the buffer overflow probability appears in the queuing theory for different communication network models. The tasks of such type were solved for many types of processes, including Gaussian ones and aforementioned FBM (see, for example, Norros [1], Michna [2], Baldi and Pacchiarotti [3], etc.)....

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