Geodesic
On convergence of distributions of compound Cox processes to stable laws
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 4, pp. 786-792 Cet article a éte moissonné depuis la source Math-Net.Ru

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Necessary and sufficient conditions are presented for weak convergence of one-dimensional distributions of compound doubly stochastic Poisson processes in which jumps have finite variances, whereas no moment-type restrictions are imposed on the controlling process. Criteria of convergence of distributions of these processes to stable laws are presented.
Keywords: doubly stochastic Poisson process (Cox process), compound Cox process, heavy tails, strictly stable distribution. 
@article{TVP_1998_43_4_a11,
     author = {V. Yu. Korolev},
     title = {On convergence of~distributions of~compound {Cox} processes to~stable laws},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {786--792},
     year = {1998},
     volume = {43},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_4_a11/}
}
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V. Yu. Korolev. On convergence of distributions of compound Cox processes to stable laws. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 4, pp. 786-792. http://geodesic.mathdoc.fr/item/TVP_1998_43_4_a11/