Mouvement brownien et espaces de besov

Abstract

Let be a linear brownian motion. Traditionally, this brownian motion is considered as a process which belongs a.s. to the space of continuous functions defined on [01], vanishing at the origin and endowed with the topology of uniform convergence. Let now be the besov space of the functions defined on [01], . They are spaces of sequences and an important fact is therefore that these Besov spaces are isomorphic to suitable Banach spaces of numerical sequences. This property is particularly well adapted to the study of brownian motion considered as a process which belongs a.s.to the spaces In this article we illustrate this in the following situations:Z. Ciesielski fias shown recently [C3] that brownian motion belongs a.s. to the space There we characterize in this first paragraph the set indexes αp, qsuch that brownian motion belongs a.s. to The classical theory of large deviations gives the behaviour, as ,of where Γ is a Borel set of the uniform topology. In the second paragraph we show that if Γ are chose...