Abstract:
We find the asymptotics for the logarithm of the Laplace transform of the
distribution of a compound renewal process as time increases unboundedly.
It is assumed that the elements of the governing
sequences of the renewal process satisfy Cramér's moment condition.
Representations for the deviation rate function of the compound renewal
process are found.
Keywords:
compound renewal process, large deviations, large deviation principle, Cramér's condition, deviation rate function, Legendre transform,
Laplace transform asymptotics.
Citation:
A. A. Borovkov, A. A. Mogul'skii, E. I. Prokopenko, “Properties of the deviation rate function and the asymptotics for the Laplace thansform of the distribution of a compound renewal process”, Teor. Veroyatnost. i Primenen., 64:4 (2019), 625–641; Theory Probab. Appl., 64:4 (2020), 499–512
\Bibitem{BorMogPro19}
\by A.~A.~Borovkov, A.~A.~Mogul'skii, E.~I.~Prokopenko
\paper Properties of the deviation rate function and the asymptotics for the Laplace thansform of the distribution of a compound renewal process
\jour Teor. Veroyatnost. i Primenen.
\yr 2019
\vol 64
\issue 4
\pages 625--641
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\transl
\jour Theory Probab. Appl.
\yr 2020
\vol 64
\issue 4
\pages 499--512
\crossref{https://doi.org/10.1137/S0040585X97T989660}
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Linking options:
https://www.mathnet.ru/eng/tvp5285
https://doi.org/10.4213/tvp5285
https://www.mathnet.ru/eng/tvp/v64/i4/p625
This publication is cited in the following 8 articles:
A. V. Logachov, A. A. Mogul'skii, “Large deviation principles for the processes admitting embedded compound renewal processes”, Siberian Math. J., 63:1 (2022), 119–137
A. A. Mogul'skiǐ, E. I. Prokopenko, “The Large Deviation Principle for Finite-Dimensional Distributions of Multidimensional Renewal Processes”, Sib. Adv. Math., 31:3 (2021), 188
A. A. Mogulskii, E. I. Prokopenko, “Printsip bolshikh uklonenii dlya konechnomernykh raspredelenii mnogomernykh obobschennykh protsessov vosstanovleniya”, Matem. tr., 23:2 (2020), 148–176
A. V. Logachev, A. A. Mogulskii, “Lokalnye teoremy dlya konechnomernykh priraschenii arifmeticheskikh mnogomernykh obobschennykh protsessov vosstanovleniya pri vypolnenii usloviya Kramera”, Sib. elektron. matem. izv., 17 (2020), 1766–1786
A. A. Borovkov, “Tochnaya asimptotika preobrazovaniya Laplasa nad raspredeleniem obobschennogo protsessa vosstanovleniya i svyazannye s nei zadachi”, Sib. elektron. matem. izv., 17 (2020), 824–839
A. A. Mogulskii, E. I. Prokopenko, “Funktsiya uklonenii i bazovaya funktsiya dlya mnogomernogo obobschennogo protsessa vosstanovleniya”, Sib. elektron. matem. izv., 16 (2019), 1449–1463
A. A. Mogulskii, E. I. Prokopenko, “Printsip bolshikh uklonenii v fazovom prostranstve dlya mnogomernogo pervogo obobschennogo protsessa vosstanovleniya”, Sib. elektron. matem. izv., 16 (2019), 1464–1477
A. A. Mogulskii, E. I. Prokopenko, “Printsip bolshikh uklonenii v fazovom prostranstve dlya mnogomernogo vtorogo obobschennogo protsessa vosstanovleniya”, Sib. elektron. matem. izv., 16 (2019), 1478–1492
Citation in format AMSBIB
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