Taylor Based Jump Diffusion Model of Fractional Brownian Motion of Stock Price

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.

Simulation of fractional Brownian motion

Preface In recent years, there has been great interest in the simulation of long-range dependent processes, in particular fractional Brownian motion. Motivated by applications in communications engineering, I wrote my master's thesis on the subject in 2002. Since many people turned out to be interested in various aspects of fractional Brownian motion, I decided to update my thesis and make it p...

Estimating General Diffusion Type Process Driven by Fractional Brownian Motion

Conventions and Notations (1) The measure space (M;M; d ) is interpreted as having M as the underly set, M the sigma algebra on M , and d the mesaure on M: If M is a metric space then M is taken as the sigma algebra generated by all its metric-open sets. (2) For two measure spaces (M;M; d ) ; (M1;M1; d 1) and (M M1;M M1; d d 1) is their product measure space. All measurs in the paper are consid...

Tempered fractional Brownian motion

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion