APPLYING RESAMPLING TO RANDOM PROCESSES PROBLEMS

                     Oleg Seleznjev

                Moscow State University

We introduce the notion of weakly approaching and conditionally
weakly approaching  sequences of random processes. This notion
generalizes the conventional weak convergence and it has been
proposed for real valued random variables in Belyaev (1995).
Some of the standard tools (e.g., Continuous Mapping Theorem)
for an investigation of behavior of weak approaching sequences
of random elements in metric spaces are developed. The spaces of
smoothed and right continuous functions with left-hand limits are
considered. This technique allows to use  the resampling approach
for an evaluation of distributions of certain continuous
functionals on realizations of random processes. Two numerical
examples are given for such functionals as supremum and number of
crossings of some level by the sum of independent random processes.

Belyaev, Yu.K. (1995). Bootstrap, Resampling and Mallows Metric.
Lecture Notes 1, Department of Mathematical Statistics, Umeå
University