Large deviation for stochastic volterra equation in the Besov-Orlicz space and application

In this paper, we firstly study the regularity of solution to R d -valued stochastic Volterra equation by proving that they almost surely belong to the Besov-Orlicz spaces corresponding to the Young function M 2 ( t ) = exp( t 2 )− 1 and the modulus of continuity Secondly, we establish a large deviation principle for solution to multidimensional stochastic Volterra equations in this space, which generalizes the result in Nualart and Rovira (2000) [16] dealing with the uniform topology, weaker than the Besov-Orlicz One. Finally, as an application we give an example of interest: a stochastic di®erential equation driven by fBm .