Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 122-132
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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/
@article{ZNSL_2015_442_a7,
author = {O. V. Rusakov},
title = {Tightness of the sums of independent identically distributed pseudo-poissonian processes in the {Skorokhod} space},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {122--132},
year = {2015},
volume = {442},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a7/}
}
TY - JOUR
AU - O. V. Rusakov
TI - Tightness of the sums of independent identically distributed pseudo-poissonian processes in the Skorokhod space
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2015
SP - 122
EP - 132
VL - 442
UR - http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a7/
LA - ru
ID - ZNSL_2015_442_a7
ER -
%0 Journal Article
%A O. V. Rusakov
%T Tightness of the sums of independent identically distributed pseudo-poissonian processes in the Skorokhod space
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 122-132
%V 442
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a7/
%G ru
%F ZNSL_2015_442_a7
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.
