The rate function and the fundamental function for multidimensional compound renewal process

DOI10.33048/semi.2019.16.100zbMath1423.60131OpenAlexW3016207784MaRDI QIDQ2334780

Evgeniĭ Igor'evich Prokopenko, Anatoliĭ Alfredovich Mogul'skiĭ

Publication date: 7 November 2019

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

Full work available at URL: https://doi.org/10.33048/semi.2019.16.100

zbMATH Keywords

large deviationsCramer conditionfundamental functionLegendre transformationdeviation (rate) functioncompound multidimensional renewal process

Mathematics Subject Classification ID

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

Related Items (9)

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 ⋮ 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 ⋮ Limit theorems for the maximal path weight in a directed graph on the line with random weights of edges ⋮ Large deviation principles for the processes admitting embedded compound renewal processes ⋮ 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 ⋮ Принцип больших уклонений для конечномерных распределений многомерных обобщенных процессов восстановления

Cites Work

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• From uniform renewal theorem to uniform large and moderate deviations for renewal-reward processes
• The second rate function and the asymptotic problems of renewal and hitting the boundary for multidimensional random walks
• Integro-local limit theorems for compound renewal processes under Cramér's condition. II
• 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 principle for multidimensional first compound renewal processes in the phase space
• Large deviation principle for multidimensional second compound renewal processes in the phase space
• Properties of the Deviation Rate Function and the Asymptotics for the Laplace Transform of the Distribution of a Compound Renewal Process
• Convex Analysis
• Large deviations for renewal processes

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