A version of Hörmander’s theorem for 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

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the c...

Central limit theorem for an additive functional of the fractional Brownian motion II ∗

We prove a central limit theorem for an additive functional of the d-dimensional fractional Brownian motion with Hurst index H ∈ ( 1 d+2 , 1 d ), using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.

On Gaussian Processes Equivalent in Law to Fractional Brownian Motion

We consider Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. We prove a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index H [ 2 . For the case H> 2 we show that such a representation cannot hold. We also consider briefly the connection between Hitsuda and Girsanov representations. Using the...