Generalized Arcsine Laws for Fractional Brownian Motion

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.)....

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

Stochastic Integration for Tempered Fractional Brownian Motion.

Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus.

Extending self-similarity for fractional Brownian motion

The fractional Brownian motion (fBm) model has proven to be valuable in modeling many natural processes because of its persistence for large time lags. However, the model is characterized by one single parameter that cannot distinguish between shortand long-term correlation effects. This work investigates the idea of extending selfsimilarity to create a correlation model that generalizes discre...