Introduction

Abstract

In the first part of these notes we consider the following class of stochastic differential equations dξ(t) = b(ξ()) dt + σ(ξ())dw(t), ξ(0) = χ∈ℝ^d, where w(t) = (w ₁ (t),... ,W _d(t)) is a standard d-dimensional Brownian motion, the vector field b : ℝ^d → ℝ^d and the matrix valued function σ : ℝ^d → ℒ(ℝ^d) are smooth and have polynomial growth together with their derivatives and b enjoys some dissipativity conditions.