On weak convergence of functionals of stochastic processes with continuously differentiable paths

We obtain a criterion for weak convergence of a sequence of stochastic processes_n(t), t [0, 1],n N,_n(t) R^m in the spaceC_m^k[0, 1] of continuously differentiable functions. We consider several examples of weakly convergent sequences of stochastic processes inC_m^k[0, 1] and several integer functionals defined on these random variables.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 85–90, 1987.