Research output: Contribution to journal › Article › peer-review
Tightness of Sums of Independent Identically Distributed Pseudo-Poisson Processes in the Skorokhod Space. / Rusakov, O. V.
In: Journal of Mathematical Sciences (United States), Vol. 225, No. 5, 01.09.2017, p. 805-811.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Tightness of Sums of Independent Identically Distributed Pseudo-Poisson Processes in the Skorokhod Space
AU - Rusakov, O. V.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85026817779&partnerID=8YFLogxK
U2 - 10.1007/s10958-017-3496-z
DO - 10.1007/s10958-017-3496-z
M3 - Article
AN - SCOPUS:85026817779
VL - 225
SP - 805
EP - 811
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 5
ER -
ID: 15542743