CONVERGENCE IN SKOROKHOD J-TOPOLOGY FOR COMPOSITIONS OF STOCHASTIC PROCESSES

D. S. SILVESTROV

Theory of Stochastic Processes Vol. 14 (30), no. 1, 2008, pp. 126–143

A survey on functional limit theorems for compositions of stochastic processes is presented. Applications to stochastic processes with random scaling of time, random sums, extremes with random sample size, generalised exceeding processes, sum- and max-processes with renewal stopping, and shock processes are discussed.


Full version