L\'evy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces

In this paper we investigate the existence and some useful properties of the L\'evy areas of Ornstein-Uhlenbeck processes associated to Hilbert-space-valued fractional Brownian-motions with Hurst parameter $H\in (1/3,1/2]$. We prove that this stochastic area has a H\"older-continuous version with sufficiently large H\"older-exponent and that can be approximated by smooth areas. In addition, we prove the stationarity of this area.Comment: 18 page

On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions

We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a tool, we define a new function of two complex variables, which is a natural generalization of the classical Gamma function for the setting we conside

Parameter estimations for SPDEs with multiplicative fractional noise

We study parameter estimation problem for diagonalizable stochastic partial differential equations driven by a multiplicative fractional noise with any Hurst parameter $H\in(0,1)$. Two classes of estimators are investigated: traditional maximum likelihood type estimators, and a new class called closed-form exact estimators. Finally the general results are applied to stochastic heat equation driven by a fractional Brownian motion