Abstract
A number of results supplementing the well-known large deviation principle for com¬pound renewal processes is obtained.
Similar content being viewed by others
References
A. A. Borovkov and A. A. Mogul’skii, “Large deviation principles for the finite-dimensional distributions of compound renewal processes,” Sibirsk. Mat. Zh. 56 (1), 36–64 (2015) [Sib. Math. J. 56 (1), 28-53 (2015)].
J. Feng and T. G. Kurtz, Large Deviations for Stochastic Processes, in Math. Surveys Monogr. (Amer. Math. Soc., Providence, RI, 2006), Vol. 131.
P. Ney and T. Nummelin, “Markov additive processes. I. Eigenvalue properties and limit theorems,” Ann. Probab. 15 (2), 561–592(1987).
P. Ney and T. Nummelin, “Markov additive processes. II. Large deviations,” Ann. Probab. 15 (2), 593–609 (1987).
C. Macci, “Large deviations for compound Markov renewal processes with dependent jumps sizes and jump waiting times,” Bull. Belg. Math. Soc. Simon Stevin 14 (2), 213–228 (2007).
R. Rockafellar, Convex Analysis (Princeton University Press, Princeton, NJ, 1970; Mir, Moscow, 1973).
A. A. Borovkov, Asymptotic Analysis of Random Walks. Rapidly Decreasing Distributions of Increments (Fizmatlit, Moscow, 2013) [in Russian].
A. A. Borovkov and A. A. Mogul’skii, “Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case,” Mat. Tr. 17 (2), 84–101 (2014) [Siberian Adv. Math. 25 (4), 255-267 (2015)].
A. A. Borovkov, “Large deviation principles in boundary problems for compound renewal processes,” Sibirsk. Mat. Zh. 57 (3), 562–595 (2016) [Sib. Math. J. 57 (3), 442-469 (2016)].
Funding
This work was supported in part by the Program for Basic Research SO RAN no. I.1.3 (grant no. 0314-2016-0008) as well as by the Russian Foundation for Basic Research under grant 18-01-00101a.
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 6, pp. 811-820.
Rights and permissions
About this article
Cite this article
Borovkov, A.A. On Large Deviation Principles for Compound Renewal Processes. Math Notes 106, 864–871 (2019). https://doi.org/10.1134/S000143461911021X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S000143461911021X