Large deviation principles in boundary problems for compound renewal processes

DOI10.1134/S003744661603006XzbMath1382.60052OpenAlexW2468454300MaRDI QIDQ311242

Aleksandr A. Borovkov

Publication date: 29 September 2016

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

Full work available at URL: https://doi.org/10.1134/s003744661603006x

zbMATH Keywords

large deviation principleboundary problemcompound renewal processadmissible nonhomogeneityfirst boundary problemlevel curvesregular deviationsecond boundary problemsecond deviation functionshortest trajectory

Mathematics Subject Classification ID

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

Related Items (12)

Local theorems for arithmetic compound renewal processes when Cramer's condition holds ⋮ Integro-local limit theorems for compound renewal processes under Cramér's condition. I ⋮ Локальные теоремы для арифметических многомерных обобщенных процессов восстановления при выполнении условия Крамера ⋮ Integro-local theorems in boundary crossing problems for compound renewal processes ⋮ Large deviation principles for renewal-reward processes ⋮ Boundary crossing problems for compound renewal processes ⋮ On a Property of the Legendre Transform ⋮ Local theorems for finite-dimensional increments of compound multidimensional arithmetic renewal processes with light tails ⋮ Extension of the Invariance Principle for Compound Renewal Processes to the Zones of Moderately Large and Small Deviations ⋮ 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 ⋮ On large deviation principles for compound renewal processes

Cites Work

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• The second rate function and the asymptotic problems of renewal and hitting the boundary for multidimensional random walks
• Functional large deviation principles for first-passage-time processes
• Large deviation principles for the finite-dimensional distributions of compound renewal processes
• Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case
• Asymptotic Analysis of Random Walks
• Large Deviations for Trajectories of Multi-Dimensional Random Walks

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