Tightness of Sums of Independent Identically Distributed Pseudo-Poisson Processes in the Skorokhod Space
| Autor: | O. V. Rusakov |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Pure mathematics Sequence Weak convergence Subordinator Applied Mathematics General Mathematics 010102 general mathematics Mathematical analysis Poisson distribution 01 natural sciences 010305 fluids & plasmas Skorokhod integral symbols.namesake Compact space Mathematics::Probability 0103 physical sciences symbols 0101 mathematics Random variable Mathematics Central limit theorem |
| Zdroj: | Journal of Mathematical Sciences. 225:805-811 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-017-3496-z |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|