Integro-Local Limit Theorems for Compound Renewal Processes under Cramér’S Condition. I
- Authors: Borovkov A.A.1, Mogulskii A.A.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 59, No 3 (2018)
- Pages: 383-402
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171845
- DOI: https://doi.org/10.1134/S0037446618030023
- ID: 171845
Cite item
Abstract
We obtain integro-local limit theorems in the phase space for compound renewal processes under Cramér’s moment condition. These theorems apply in a domain analogous to Cramér’s zone of deviations for random walks. It includes the zone of normal and moderately large deviations. Under the same conditions we establish some integro-local theorems for finite-dimensional distributions of compound renewal processes.
About the authors
A. A. Borovkov
Sobolev Institute of Mathematics
Author for correspondence.
Email: borovkov@math.nsc.ru
Russian Federation, Novosibirsk
A. A. Mogulskii
Sobolev Institute of Mathematics
Email: borovkov@math.nsc.ru
Russian Federation, Novosibirsk