Geodesic
Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments
Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 45-68.

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

We extend the large deviation principles for random walks and processes with independent increments to the case of conditional probabilities given that the position of the trajectory at the last time moment is localized in a neighborhood of some point. As a corollary, we obtain a moderately large deviation principle for empirical distributions (an analog of Sanov's theorem). 
@article{MT_2013_16_2_a3,
     author = {A. A. Borovkov and A. A. Mogul'skiǐ},
     title = {Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments},
     journal = {Matemati\v{c}eskie trudy},
     pages = {45--68},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2013_16_2_a3/}
}
TY  - JOUR
AU  - A. A. Borovkov
AU  - A. A. Mogul'skiǐ
TI  - Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments
JO  - Matematičeskie trudy
PY  - 2013
SP  - 45
EP  - 68
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2013_16_2_a3/
LA  - ru
ID  - MT_2013_16_2_a3
ER  - 
%0 Journal Article
%A A. A. Borovkov
%A A. A. Mogul'skiǐ
%T Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments
%J Matematičeskie trudy
%D 2013
%P 45-68
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2013_16_2_a3/
%G ru
%F MT_2013_16_2_a3
A. A. Borovkov; A. A. Mogul'skiǐ. Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments. Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 45-68. http://geodesic.mathdoc.fr/item/MT_2013_16_2_a3/

[1] Borovkov A. A., “Granichnye zadachi dlya sluchainykh bluzhdanii i bolshie ukloneniya v funktsionalnykh prostranstvakh”, TVP, 12:4 (1967), 635–654 | MR | Zbl

[2] Borovkov A. A., Teoriya veroyatnostei, Uchebnoe posobie, 5-e izd. (suschestvenno pererab. i dop.), Knizhnyi dom “Librokom”, M., 2009

[3] Borovkov A. A., Borovkov K. A., Asimptoticheskii analiz sluchainykh bluzhdanii, v. 1, Medlenno ubyvayuschie raspredeleniya skachkov, Fizmatlit ANO, M., 2008

[4] Borovkov A. A., Mogulskii A. A., “Integro-lokalnye i integralnye teoremy dlya summ sluchainykh velichin s semieksponentsialnymi raspredeleniyami, deistvuyuschie na vsei osi”, Sib. matem. zhurn., 47:6 (2006), 1218–1257 | MR | Zbl

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

[6] 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

[7] Borovkov A. A., Mogulskii A. A., “Printsipy bolshikh uklonenii dlya traektorii sluchainykh bluzhdanii. I”, TVP, 56:4 (2011), 627—655 ; “II”, ТВП, 57:1 (2012), 3–34 ; “III”, ТВП, 58:1 (2013), 37–52 | DOI | DOI | Zbl | DOI

[8] Borovkov A. A., Mogulskii A. A., “Printsipy umerenno bolshikh uklonenii dlya traektorii sluchainykh bluzhdanii i protsessov s nezavisimymi prirascheniyami”, TVP, 58:4 (2013) (to appear)

[9] Ibragimov I. A., Linnik Yu. V., Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965

[10] Mogulskii A. A., “Bolshie ukloneniya dlya traektorii mnogomernykh sluchainykh bluzhdanii”, TVP, 21:2 (1976), 309–323 | MR | Zbl

[11] Nagaev S. V., “Nekotorye predelnye teoremy dlya bolshikh uklonenii”, TVP, 10:2 (1965), 231–254 | MR | Zbl

[12] Nagaev A. V., “Integralnye predelnye teoremy s uchetom bolshikh uklonenii, kogda ne vypolneno uslovie Kramera. I”, TVP, 14:1 (1969), 51–63 | MR | Zbl

[13] Petrov V. V., “Predelnye teoremy dlya bolshikh uklonenii pri narushenii usloviya Kramera. I”, Vestn. LGU, 1963, no. 19, 49–68 | Zbl

[14] Rozovskii L. V., “Veroyatnosti bolshikh uklonenii na vsei osi”, TVP, 38:1 (1993), 79–109 | MR | Zbl

[15] Saulis L., Statulyavichus V., Predelnye teoremy o bolshikh ukloneniyakh, Mokslas, Vilnyus, 1989 | MR | Zbl

[16] Mikosh T., Nagaev A. V., “Large deviations of heavy-tailed sums with applications in insurance”, Extremes, 1:1 (1998), 81–110 | DOI | MR

[17] Stone C., “On local and ratio limit theorems”, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability, Part 2, v. II, Contributions to Probability Theory, Univ. California Press, Berkeley, Calif., 1965/1966, 217–224 | MR

[18] Varadhan S. R. S., “Asymptotic probabilities and differential equations”, Comm. Pure Appl. Math., 19:3 (1966), 261–286 | DOI | MR | Zbl