Integro-local limit theorems for compound renewal processes under Cramér's condition. I

DOI10.1134/S0037446618030023zbMath1404.60128OpenAlexW4252827228MaRDI QIDQ1673661

Anatoliĭ Alfredovich Mogul'skiĭ, Aleksandr A. Borovkov

Publication date: 13 September 2018

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446618030023

zbMATH Keywords

deviation functionlarge deviationscompound renewal processsecond deviation functionCramér's conditionrenewal measureintegro-local theorem

Mathematics Subject Classification ID

Large deviations (60F10) Functional limit theorems; invariance principles (60F17) Renewal theory (60K05)

Related Items (18)

Integro-local limit theorems for compound renewal processes under Cramér's condition. II ⋮ Characterization of large deviation probabilities for regenerative sequences ⋮ Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. I ⋮ 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 ⋮ Integro-local theorems in boundary crossing problems for compound renewal processes ⋮ Boundary crossing problems for compound renewal processes ⋮ Large deviations of generalized renewal process ⋮ Local theorems for finite-dimensional increments of compound multidimensional arithmetic renewal processes with light tails ⋮ Local theorems for (multidimensional) additive functionals of semi-Markov chains ⋮ Large deviations in discrete-time renewal theory ⋮ Properties of the Deviation Rate Function and the Asymptotics for the Laplace Transform of the Distribution of a Compound Renewal Process ⋮ Large deviation principles for the processes admitting embedded compound renewal processes ⋮ The rate function and the fundamental function for multidimensional compound renewal process ⋮ Large deviation principle for multidimensional first compound renewal processes in the phase space ⋮ Large deviation principle for multidimensional second compound renewal processes in the phase space ⋮ Large Deviations for a Terminating Compound Renewal Process

Cites Work

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• Large deviation principles in boundary problems for compound renewal processes
• The second rate function and the asymptotic problems of renewal and hitting the boundary for multidimensional random walks
• 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
• Convex Analysis

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