The Packing Measure of the Trajectories of Multiparameter Fractional Brownian Motion

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

Some singular sample path properties of a multiparameter fractional Brownian motion

We prove a Chung-type law of the iterated logarithm for a multiparameter extension of the fractional Brownian motion which is not increment stationary. This multiparameter fractional Brownian motion behaves very differently at the origin and away from the axes, which also appears in the Hausdorff dimension of its range and in the measure of its pointwise Hölder exponents. A functional version o...

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

An optimal series expansion of the multiparameter fractional Brownian motion ∗

We derive a series expansion for the multiparameter fractional Brownian motion. The derived expansion is proven to be rate optimal .

A family of series representations of the multiparameter fractional Brownian motion

We derive a family of series representations of the multiparameter fractional Brownian motion in the centred ball of radius R in the N-dimensional space RN . Some known examples of series representations are shown to be the members of the family under consideration.