Regularity Properties of Some Stochastic Volterra Integrals with Degenerate Kernel

We derive sampleepaths continuity results for some sto-chastic Volterra integrals with degenerate kernel under integrability assumptions on the integrand. Some applications to processes arising in the analysis of the fractional Brownian motion are given. Embeddings of Besov spaces into sets of HHlder continuous functions are the key elements. RRSUMM. Nous montrons la continuitt trajectorielle d'inttgrales sto-chastiques de type Volterra avec noyaux irrrguliers. Nous appliquons ce rrsultat des processus liis au mouvement Brownien fractionnaire. En corollaire, on obtient des inngalitts maximales pour des processus qui ne sont pas des martingales. Pour ce faire, on utilise des injections d'espaces de Besov dans l'ensemble des fonctions HHlddriennes. 1. Introduction In the analysis of the fractional Brownian motion, some stochastic Volterra integrals with degenerate and nonnconvolutional kernels appear naturally see below Section 4. Several papers do exist on the sampleepaths regularity properties of stochastic Volterra integrals but always with regular or convolu-tional kernels (see for instance 1, 3]). The goal of this paper is thus to derive some continuity results for stochastic integrals of the form