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

Результат исследований: Научные публикации в периодических изданияхстатья

Выдержка

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.

Язык оригиналаанглийский
Страницы (с-по)805-811
Число страниц7
ЖурналJournal of Mathematical Sciences (United States)
Том225
Номер выпуска5
DOI
СостояниеОпубликовано - 1 сен 2017

Отпечаток

Tightness
Poisson process
Random variables
Identically distributed
Relative Compactness
Random Sums
Subordinator
I.i.d. Random Variables
Weak Convergence
Central limit theorem
Family

Предметные области Scopus

  • Теория вероятности и статистика
  • Математика (все)
  • Прикладная математика

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Tightness of Sums of Independent Identically Distributed Pseudo-Poisson Processes in the Skorokhod Space. / Rusakov, O. V.

В: Journal of Mathematical Sciences (United States), Том 225, № 5, 01.09.2017, стр. 805-811.

Результат исследований: Научные публикации в периодических изданияхстатья

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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.

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