STRONG INVARIANCE PRINCIPLE FOR A SUPERPOSITION OF RANDOM PROCESSES

N. M. ZINCHENKO

Theory of Stochastic Processes

Vol.16 (32), no.1, 2010, pp.130-138

The strong invariance principle (SIP) is proved for a superposition of random processes S(N(t)) under rather general assumptions on S(t) and N(t). As a consequence, a number of SIP-type results are obtained for random sums and used to investigate their rate of growth and fluctuation of increments.