Abstract:
We obtain the large deviation principles for multidimensional second compound renewal processes Y(t) in the phase space Rd, for this we find and investigate the rate function DY(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 AY(μ).
Keywords:
compound multidimensional renewal process, large deviations, renewal measure, Cramer's condition, deviation (rate) function, second deviation (rate) function.
Citation:
A. A. Mogulskii, E. I. Prokopenko, “Large deviation principle for multidimensional second compound renewal processes in the phase space”, Sib. Èlektron. Mat. Izv., 16 (2019), 1478–1492
\Bibitem{MogPro19}
\by A.~A.~Mogulskii, E.~I.~Prokopenko
\paper Large deviation principle for multidimensional second compound renewal processes in the phase space
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1478--1492
\mathnet{http://mi.mathnet.ru/semr1143}
\crossref{https://doi.org/10.33048/semi.2019.16.102}
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https://www.mathnet.ru/eng/semr1143
https://www.mathnet.ru/eng/semr/v16/p1478
This publication is cited in the following 7 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
Mogulskii A.A., Prokopenko E.I., “the Rate Function and the Fundamental Function For Multidimensional Compound Renewal Process”, Sib. Electron. Math. Rep., 16 (2019), 1449–1463
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