Stochastic integration with respect to the fractional Brownian motion

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

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

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 .

Integration with Respect to Fractional Local times with Hurst Index

In this paper, we study the stochastic integration with respect to local times of fractional Brownian motion B with Hurst index 1/2 < H < 1. As a related problem we define the weighted quadratic covariation [f(B), B ] ) of f(B) and B as follows n−1

Stochastic Integration with respect to Volterra processes

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 ...