Geodesic
On asymptotic behaviour of probabilities of large and moderate deviations for some iterated stochastic processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 229-242 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We derive logarithmic asymptotics for probabilities of large deviations for some iterated processes. We show that under appropriate conditions, these asymptotics are the same as those for sums of independent random variables. When these conditions do not hold, the asymptotics of large deviations for the iterated processes are quite different. When the iterated process is a homogeneous process with independent increments, in which time is replaced by a random one, the behaviour of large and moderate deviations are investigated in the case of finite variance. For this case, the following one-sided moment restriction are considered: the Cramèr condition, the Linnik condition, the existence of moment of order $p>2$ for a positive part. Bibl. – 6 titles. 
@article{ZNSL_2009_368_a16,
     author = {A. N. Frolov},
     title = {On asymptotic behaviour of probabilities of large and moderate deviations for some iterated stochastic processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {229--242},
     year = {2009},
     volume = {368},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a16/}
}
TY  - JOUR
AU  - A. N. Frolov
TI  - On asymptotic behaviour of probabilities of large and moderate deviations for some iterated stochastic processes
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 229
EP  - 242
VL  - 368
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a16/
LA  - ru
ID  - ZNSL_2009_368_a16
ER  - 
%0 Journal Article
%A A. N. Frolov
%T On asymptotic behaviour of probabilities of large and moderate deviations for some iterated stochastic processes
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 229-242
%V 368
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a16/
%G ru
%F ZNSL_2009_368_a16
A. N. Frolov. On asymptotic behaviour of probabilities of large and moderate deviations for some iterated stochastic processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 229-242. http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a16/

[1] A. N. Frolov, “Ob asimptoticheskom povedenii veroyatnostei bolshikh uklonenii obobschennykh protsessov Koksa”, Zap. nauchn. semin. POMI, 361, 2008, 167–181

[2] A. N. Frolov, “Ob asimptoticheskom povedenii veroyatnostei umerennykh uklonenii”, Trudy Sankt-Peterburgskogo mat. obschestva, 14, 2008, 197–211

[3] A. N. Frolov, “Universalnye predelnye teoremy dlya priraschenii protsessov s nezavisimymi prirascheniyami”, Teoriya veroyatn. i ee primen., 49:3 (2004), 601–609 | DOI | MR | Zbl

[4] W. Feller, “Limit theorems for probabilities of large deviations”, Z. Wahrscheinlichkeitstheor. verw. Geb., 14 (1969), 1–20 | DOI | MR | Zbl

[5] V. V. Petrov, Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972 | MR

[6] A. N. Frolov, “O veroyatnostyakh umerennykh uklonenii summ nezavisimykh sluchainykh velichin”, Zap. nauchn. semin. POMI, 294, 2002, 200–215 | MR | Zbl