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Convergence in Skorokhod \(J\)-topology for compositions of stochastic processes. (English) Zbl 1199.60103

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
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