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Theory of Stochastic Processes, 2008, Volume 14(30), Issue 1, Pages 126–143 (Mi thsp136)  
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
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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.
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Document Type: Article
MSC: 60F17
Language: English
Citation: D. S. Silvestrov, “Convergence in skorokhod $J$-topology for compositions of stochastic processes”, Theory Stoch. Process., 14(30):1 (2008), 126–143
Citation in format AMSBIB
\Bibitem{Sil08}
\by D.~S.~Silvestrov
\paper Convergence in skorokhod $J$-topology for
compositions of stochastic processes
\jour Theory Stoch. Process.
\yr 2008
\vol 14(30)
\issue 1
\pages 126--143
\mathnet{http://mi.mathnet.ru/thsp136}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2479713}
\zmath{https://zbmath.org/?q=an:1199.60103}
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