| Title:
|
On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums (English) |
| Author:
|
Hung, Tran Loc |
| Author:
|
Kien, Phan Tri |
| Author:
|
Nhut, Nguyen Tan |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
55 |
| Issue:
|
6 |
| Year:
|
2019 |
| Pages:
|
961-975 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the Zolotarev probability metric, the rates of convergence in some weak limit theorems for geometric random sums are estimated. (English) |
| Keyword:
|
geometric random sums |
| Keyword:
|
Gnedenko's transfer theorem |
| Keyword:
|
Zolotarev probability metric |
| MSC:
|
60E07 |
| MSC:
|
60F05 |
| MSC:
|
60F99 |
| MSC:
|
60G50 |
| idZBL:
|
Zbl 07217221 |
| idMR:
|
MR4077139 |
| DOI:
|
10.14736/kyb-2019-6-0961 |
| . |
| Date available:
|
2020-05-20T15:13:28Z |
| Last updated:
|
2020-08-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148086 |
| . |
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