Comportement asymptotique de la solution d'une sorte d'équation intégrale stochastique dans $R^n$. [Asymptotic behavior of the solution of a certain stochastic integral equation in $R^n$]

We consider a stochastic integral equation in ${\bbfR}^n$, i.e, integral equation to which a stochastic perturbation is added. In the first part we consider the linear equation with constant coefficients. For this equation, first of all, we establish the uniform boundedness of the solution and, by using this uniform boundedness and by considering the solution in a suitable Hilbert space, we prove the existence of an invariant measure for this equation; the invariant measure will be proved to be unique. In the second part we consider the nonlinear equation with suitable conditions and, by using a method developed for the linear equation, we prove the existence of an invariant measure for this nonlinear equation.