Abstract
In the work, which consists of 4 papers (the article and [15]-[17]), we obtain integro-local limit theorems in the phase space for multidimensional compound renewal processes, when Cramer's condition holds. In the part I (the article) we consider the so-called first renewal process Z(t) in a regular region, which is an of analog Cramer's deviation region for random walk. The regular region includes normal and moderate deviations.
| Translated title of the contribution | Интегро-локальные теоремы для многомерных обобщенных процессов восстановления при моментном условии Крамера. I |
|---|---|
| Original language | English |
| Pages (from-to) | 475-502 |
| Number of pages | 28 |
| Journal | Сибирские электронные математические известия |
| Volume | 15 |
| DOIs | |
| Publication status | Published - 1 Jan 2018 |
Keywords
- compound multidimensional renewal process
- first (second) renewal process
- large deviations
- integro-local limit theorems
- renewal measure
- Cramer's condition
- deviation (rate) function
- second deviation (rate) function
State classification of scientific and technological information
- 27.43 Probability Theory and mathematical statistics