Weak invariance principle for solutions of stochastic recurrence equations in a banach space

We show that, in a Banach space, continuous random processes constructed by using solutions of the difference equationX_n=A_nX_n+1+V_n, n=1, 2,..., converge in distribution to a solution of the corresponding operator equation.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 114–117, January, 1995.