Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. I

zbMath1395.60102MaRDI QIDQ1669911

Anatoliĭ Alfredovich Mogul'skiĭ, Evgeniĭ Igor'evich Prokopenko

Publication date: 4 September 2018

Published in: Sibirskie Èlektronnye Matematicheskie Izvestiya (Search for Journal in Brave)

zbMATH Keywords

large deviationsCramer's conditionintegro-local limit theoremsrenewal measurecompound multi-dimensional renewal processdeviation (rate) functionfirst (second) renewal processsecond deviation (rate) function

Mathematics Subject Classification ID

Large deviations (60F10) Renewal theory (60K05)

Related Items (11)

Characterization of large deviation probabilities for regenerative sequences ⋮ Local theorems for arithmetic compound renewal processes when Cramer's condition holds ⋮ Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. II ⋮ Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. III ⋮ Локальные теоремы для арифметических многомерных обобщенных процессов восстановления при выполнении условия Крамера ⋮ Large deviation principle for terminating multidimensional compound renewal processes with application to polymer pinning models ⋮ Large deviations of generalized renewal process ⋮ Local theorems for (multidimensional) additive functionals of semi-Markov chains ⋮ Large deviation principle for multidimensional first compound renewal processes in the phase space ⋮ Large Deviations for a Terminating Compound Renewal Process ⋮ Принцип больших уклонений для конечномерных распределений многомерных обобщенных процессов восстановления

Cites Work

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• The second rate function and the asymptotic problems of renewal and hitting the boundary for multidimensional random walks
• Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. II
• Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. III
• Integro-local limit theorems for compound renewal processes under Cramér's condition. I
• Probability theory. Edited by K. A. Borovkov. Transl. from the Russian by O. Borovkova and P. S. Ruzankin
• Large deviation principles for the finite-dimensional distributions of compound renewal processes
• Integro-Local Limit Theorems for Compound Renewal Processes
• A Local Limit Theorem for Nonlattice Multi-Dimensional Distribution Functions

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