Silvestrov, D. S. Convergence in Skorokhod \(J\)-topology for compositions of stochastic processes. (English) Zbl 1199.60103 Theory Stoch. Process. 14(30), No. 1, 126-143 (2008). Summary: 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. MSC: 60F17 Functional limit theorems; invariance principles 60-02 Research exposition (monographs, survey articles) pertaining to probability theory Keywords:\(J\)-topology; composition of stochastic processes; functional limit theorem; random sum; random scaling of time; generalised exceeding process; renewal-type stopping × Cite Format Result Cite Review PDF