Geodesic
Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case
Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 84-101.

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

Under the inhomogeneous case wemean the case when one or several (arbitrarily many) inhomogeneous summands are added to the sum of independent identically distributed vectors. We find necessary and sufficient conditions under which the large deviation principles for such sums and the corresponding renewal functions have the same form that in the homogeneous case. 
@article{MT_2014_17_2_a4,
     author = {A. A. Borovkov and A. A. Mogul'skiǐ},
     title = {Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case},
     journal = {Matemati\v{c}eskie trudy},
     pages = {84--101},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2014_17_2_a4/}
}
TY  - JOUR
AU  - A. A. Borovkov
AU  - A. A. Mogul'skiǐ
TI  - Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case
JO  - Matematičeskie trudy
PY  - 2014
SP  - 84
EP  - 101
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2014_17_2_a4/
LA  - ru
ID  - MT_2014_17_2_a4
ER  - 
%0 Journal Article
%A A. A. Borovkov
%A A. A. Mogul'skiǐ
%T Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case
%J Matematičeskie trudy
%D 2014
%P 84-101
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2014_17_2_a4/
%G ru
%F MT_2014_17_2_a4
A. A. Borovkov; A. A. Mogul'skiǐ. Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case. Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 84-101. http://geodesic.mathdoc.fr/item/MT_2014_17_2_a4/

[1] Borovkov A. A., Mogulskii A. A., “Vtoraya funktsiya uklonenii i asimptoticheskie zadachi vosstanovleniya i dostizheniya granitsy dlya mnogomernykh bluzhdanii”, Sib. matem. zhurn., 37:4 (1996), 745–782 | MR | Zbl

[2] Borovkov A. A., Mogulskii A. A., “Integro-lokalnye predelnye teoremy dlya summ sluchainykh vektorov, vklyuchayuschie bolshie ukloneniya. II”, TVP, 45:1 (2000), 5–29 | DOI | MR | Zbl

[3] Borovkov A. A., Mogulskii A. A., “O printsipakh bolshikh uklonenii v metricheskikh prostranstvakh”, Sib. matem. zhurn., 51:6 (2010), 1251–1269 | MR | Zbl

[4] Borovkov A. A., Mogulskii A. A., “Eksponentsialnye neravenstva chebyshevskogo tipa dlya summ sluchainykh vektorov i dlya traektorii sluchainykh bluzhdanii”, TVP, 56:1 (2011), 3–29 | DOI | MR | Zbl

[5] Borovkov A. A., Mogulskii A. A., “Printsipy bolshikh uklonenii dlya konechnomernykh raspredelenii obobschennykh protsessov vosstanovleniya”, Sib. matem. zhurn. (to appear)

[6] Koks D. R., Smit V. L., Teoriya vosstanovleniya, Izd-vo “Sovetskoe radio”, M., 1967 | MR

[7] Asmussen S., Albrecher H., Ruin Probabilities, World Scientific Publishing Co., Hackensack, NJ, 2010 | MR | Zbl