Arnaud De La Pradelle

On Fractional Brownian Processes

We use Liouville spaces in order to prove the existence of some different fractional α-Brownian motion ( 0 < α ≤ 1 ), or fractional ( α, β )-Brownian sheets. There are also applications to the Wiener stochastic integral with respect to these α-Brownian.

Opérateurs linéaires gaussiens

We extend operators from the Cameron-Martin space to Gaussian Lusinian locally convex space. We then are allowed to give sense to the Mehler formula for every such bounded operator. An application is made to Hilbert-Schmidt operators. Next we show that capacities asociated to second quantizations of operators are tight on compact sets, and this is a general result even if the underlying space is not a Banach space.

Brownian processes in infinite dimension

AbstractLetE be a locally convex space endowed with a centered gaussian measure ξ. We construct a continuousE-valued brownian motionWt with covariance ξ. The main goal is to solve the SDE of Langevin type dXt=

Curvilinear Integrals Along Enriched Paths

\sqrt {2a}

A non-commutative sewing lemma.

dWt−AXt wherea andA are unbounded operators of the Cameron-Martin space of (E, ξ). It appears as the unique linear measurable extension of the solution of the classical Cauchy problemv′(t)=

On Infinite Dimensional Sheets

\sqrt {2a}