Geodesic
Convergence in skorokhod $J$-topology for
Teoriâ slučajnyh processov, Tome 14 (2008) no. 1, pp. 126-143

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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. 
@article{THSP_2008_14_1_a13,
     author = {D. S. Silvestrov},
     title = {Convergence in skorokhod $J$-topology for},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {126--143},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a13/}
}
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D. S. Silvestrov. Convergence in skorokhod $J$-topology for. Teoriâ slučajnyh processov, Tome 14 (2008) no. 1, pp. 126-143. http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a13/