Support Theorem for Random Evolution Equations in Hölderian Norm

Abstract

In this paper, we purpose to prove the support theorem of the random evolution equation where   is the solution of (E) considered as which a random-variable to value in  The coefficients σ and b satisfied Lipschitz condition and linear growth and depend to and W is a d-dimensional brownian motion. For this, we use the method of approximations of the solution of random evolution equations and extend the results well-known of diffusion processes.