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.
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Original Russian Text Copyright © 2018 Borovkov A.A. and Mogulskii A.A.
The authors were partially supported by the Russian Foundation for Basic Research (Grant 18–01–00101).
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, vol. 59, no. 3, pp. 491–513, May–June, 2018
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Borovkov, A.A., Mogulskii, A.A. Integro-Local Limit Theorems for Compound Renewal Processes under Cramér’S Condition. I. Sib Math J 59, 383–402 (2018). https://doi.org/10.1134/S0037446618030023
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DOI: https://doi.org/10.1134/S0037446618030023