Geodesic
Tightness of the sums of independent identically distributed pseudo-poissonian processes in the Skorokhod space
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 122-132 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider pseudo-poissonian process of the following simple type: it is a poissonian subordinator for a sequence of i.i.d. random variables with a finite variance. Next we consider sums of i.i.d. copies of such pseudo-poissonian process. For a family of the distributions of these random sums we prove the tightness (relative compactness) in the Skorokhod space. Under conditions of the Central Limit Theorem for vectors we obtain a weak convergence in the functional Skorokhod space of the examined sums to the Ornstein–Uhlenbeck process. 
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     title = {Tightness of the sums of independent identically distributed pseudo-poissonian processes in the {Skorokhod} space},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a7/}
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O. V. Rusakov. Tightness of the sums of independent identically distributed pseudo-poissonian processes in the Skorokhod space. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 122-132. http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a7/

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