Tightness of Sums of Independent Identically Distributed Pseudo-Poisson Processes in the Skorokhod Space

We consider a pseudo-Poisson process of the following simple type. This process is a Poissonian subordinator for a sequence of i.i.d. random variables with finite variance. Further we consider sums of i.i.d. copies of a pseudo-Poisson process. For a family of distributions of these random sums, we p...

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Veröffentlicht in:	Journal of mathematical sciences (New York, N.Y.) N.Y.), 2017-09, Vol.225 (5), p.805-811
1. Verfasser:	Rusakov, O. V.
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Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics Poisson density functions Queuing theory Random variables Sums Tightness
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description	We consider a pseudo-Poisson process of the following simple type. This process is a Poissonian subordinator for a sequence of i.i.d. random variables with finite variance. Further we consider sums of i.i.d. copies of a pseudo-Poisson process. For a family of distributions of these random sums, we prove the tightness (relative compactness) in the Skorokhod space. Under the conditions of the Central Limit Theorem for vectors, we establish the weak convergence in the functional Skorokhod space of the examined sums to the Ornstein–Uhlenbeck process.
doi_str_mv	10.1007/s10958-017-3496-z
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V.</creatorcontrib><title>Tightness of Sums of Independent Identically Distributed Pseudo-Poisson Processes in the Skorokhod Space</title><title>Journal of mathematical sciences (New York, N.Y.)</title><addtitle>J Math Sci</addtitle><description>We consider a pseudo-Poisson process of the following simple type. This process is a Poissonian subordinator for a sequence of i.i.d. random variables with finite variance. Further we consider sums of i.i.d. copies of a pseudo-Poisson process. For a family of distributions of these random sums, we prove the tightness (relative compactness) in the Skorokhod space. 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title	Tightness of Sums of Independent Identically Distributed Pseudo-Poisson Processes in the Skorokhod Space
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