Convergence in skorokhod $J$-topology for compositions of stochastic processes

D. S. Silvestrov

Department of Mathematics and Physics Mälardalen University Box 883, SE-721 23 Västerås, Sweden

Abstract: 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.

Keywords: $J$-topology, space $D$, composition of stochastic processes, functional limit theorem, random sum, random scaling of time, generalised exceeding process, renewal-type stopping.

MSC: 60F17

Language: English

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