Strong convergence of distributions of functionals of a sequence of processes,linearly generated by independent random variables

In the present paper we get sufficient conditions for the strong convergence of distributions of functionals of a sequence of stochastic processes, linearly generated by independent random variables, in the case when the distributions of these processes converge weakly to a Gaussian measure.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 122–126, 1987.