Abstract:
We obtain the large deviation principles for multidimensional first compound renewal processes Z(t) in the phase space Rd, for this we find and investigate the rate function DZ(α). Also we find asymptotics for the Laplace transform of this process when the time goes to infinity, for this we find and investigate the so-called fundamental function AZ(μ).
Keywords:
compound multidimensional renewal process, large deviations, renewal measure, Cramer's condition, deviation (rate) function, second deviation (rate) function, fundamental function.
Citation:
A. A. Mogulskii, E. I. Prokopenko, “Large deviation principle for multidimensional first compound renewal processes in the phase space”, Sib. Èlektron. Mat. Izv., 16 (2019), 1464–1477
\Bibitem{MogPro19}
\by A.~A.~Mogulskii, E.~I.~Prokopenko
\paper Large deviation principle for multidimensional first compound renewal processes in the phase space
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1464--1477
\mathnet{http://mi.mathnet.ru/semr1142}
\crossref{https://doi.org/10.33048/semi.2019.16.101}
Linking options:
https://www.mathnet.ru/eng/semr1142
https://www.mathnet.ru/eng/semr/v16/p1464
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. V. Logachov, A. A. Mogulskii, E. I. Prokopenko, “Large deviation principle for terminating multidimensional compound renewal processes with application to polymer pinning models”, Problems Inform. Transmission, 58:2 (2022), 144–159
A. Logachov, A. Mogulskii, E. Prokopenko, A. Yambartsev, “Local theorems for (multidimensional) additive functionals of semi-Markov chains”, Stoch. Process. Their Appl., 137 (2021), 149–166
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. A. Mogul'skii, A. V. Logachov, “Local Theorems For Finite-Dimensional Increments of Compound Multidimensional Arithmetic Renewal Processes With Light Tails”, Sib. Electron. Math. Rep., 17 (2020), 1766–1786
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 vtorogo obobschennogo protsessa vosstanovleniya”, Sib. elektron. matem. izv., 16 (2019), 1478–1492
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