Geodesic
On Large Deviation Principles for Compound Renewal Processes
Matematičeskie zametki, Tome 106 (2019) no. 6, pp. 811-820.

Voir la notice de l'article provenant de la source Math-Net.Ru

A number of results supplementing the well-known large deviation principle for compound renewal processes is obtained.
Keywords: compound renewal processes, large deviation principle. 
@article{MZM_2019_106_6_a1,
     author = {A. A. Borovkov},
     title = {On {Large} {Deviation} {Principles} for {Compound} {Renewal} {Processes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {811--820},
     publisher = {mathdoc},
     volume = {106},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_6_a1/}
}
TY  - JOUR
AU  - A. A. Borovkov
TI  - On Large Deviation Principles for Compound Renewal Processes
JO  - Matematičeskie zametki
PY  - 2019
SP  - 811
EP  - 820
VL  - 106
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_106_6_a1/
LA  - ru
ID  - MZM_2019_106_6_a1
ER  - 
%0 Journal Article
%A A. A. Borovkov
%T On Large Deviation Principles for Compound Renewal Processes
%J Matematičeskie zametki
%D 2019
%P 811-820
%V 106
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_106_6_a1/
%G ru
%F MZM_2019_106_6_a1
A. A. Borovkov. On Large Deviation Principles for Compound Renewal Processes. Matematičeskie zametki, Tome 106 (2019) no. 6, pp. 811-820. http://geodesic.mathdoc.fr/item/MZM_2019_106_6_a1/

[1] A. A. Borovkov, A. A. Mogulskii, “Printsipy bolshikh uklonenii dlya konechnomernykh raspredelenii obobschennykh protsessov vosstanovleniya”, Sib. matem. zhurn., 56:1 (2015), 36–64 | MR

[2] J. Feng, T. G. Kurtz, Large Deviations for Stochastic Processes, Math. Surveys Monogr., 131, Amer. Math. Soc., Providence, RI, 2006 | MR

[3] P. Ney, T. Nummelin, “Markov additive processes. I. Eigenvalue properties and limit theorems”, Ann. Probab., 15:2 (1987), 561–592 | DOI | MR

[4] P. Ney, T. Nummelin, “Markov additive processes. II. Large deviations”, Ann. Probab., 15:2 (1987), 593–609 | DOI | MR

[5] 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 (2007), 213–228 | MR

[6] R. Rokafellar, Vypuklyi analiz, Mir, M., 1973 | MR | Zbl

[7] A. A. Borovkov, Asimptoticheskii analiz sluchainykh bluzhdanii. Bystroubyvayuschie raspredeleniya priraschenii, Fizmatlit, M., 2013 | Zbl

[8] A. A. Borovkov, A. A. Mogulskii, “O printsipakh bolshikh uklonenii dlya summ sluchainykh vektorov i sootvetstvuyuschikh funktsii vosstanovleniya v neodnorodnom sluchae”, Matem. tr., 17:2 (2014), 84–101 | MR

[9] A. A. Borovkov, “Printsipy bolshikh uklonenii v granichnykh zadachakh dlya obobschennykh protsessov vosstanovleniya”, Sib. matem. zhurn., 57:3 (2016), 562–595 | DOI | MR