Weak invariance principle for solutions of stochastic recurrence equations in a banach space - Koval, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
We show that, in a Banach space, continuous random processes constructed by using solutions of the difference equationX n =A n X n+1+V n , n=1, 2,..., converge in distribution to a solution of the corresponding operator equation.