Аннотация
We continue to study the compound renewal processes under the Cramer moment condition, which was started by A.A. Borovkov and A.A. Mogulskii (2013). In the present paper we study arithmetic multidimensional compound renewal process, for which the "controlling" random vector xi = (tau, zeta) (tau > 0 determines the distance between the jumps, zeta determines the value of jumps of the compound renewal process) has an arithmetic distribution with light tails. For these processes we propose wide conditions (close to necessary), under which we can find exact asymptotics in local limit theorems for finite - dimensional increments.
Переведенное название | Local theorems for finite dimensional increments of compound multidimensional arithmetic renewal processes with light tails |
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Язык оригинала | русский |
Страницы (с-по) | 1766-1786 |
Число страниц | 21 |
Журнал | Сибирские электронные математические известия |
Том | 17 |
DOI | |
Состояние | Опубликовано - 2020 |
Ключевые слова
- compound multidimensional arithmetic renewal process
- large deviations
- moderate deviations
- renewal measure
- Cramer's condition
- rate function
- local theorems for finite - dimensional increments
- LARGE DEVIATION PRINCIPLES
- DISTRIBUTIONS
- TRAJECTORIES
- BOUNDARY
Предметные области OECD FOS+WOS
- 1.01 МАТЕМАТИКА