Limit theorems for random processes with random time substitution
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 49-58

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

In this paper we prove a theorem on sufficient conditions for the convergence in the Skorokhod space $D[0,1]$ of a sequence of random processes with random time substitution. We obtain almost certain versions of this theorem.
Keywords: Skorokhod space $D[0,1]$, random process with random time substitution, almost certain version.
E. E. Permyakova. Limit theorems for random processes with random time substitution. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 49-58. http://geodesic.mathdoc.fr/item/IVM_2008_12_a6/
@article{IVM_2008_12_a6,
     author = {E. E. Permyakova},
     title = {Limit theorems for random processes with random time substitution},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {49--58},
     year = {2008},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_12_a6/}
}
TY  - JOUR
AU  - E. E. Permyakova
TI  - Limit theorems for random processes with random time substitution
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2008
SP  - 49
EP  - 58
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/IVM_2008_12_a6/
LA  - ru
ID  - IVM_2008_12_a6
ER  - 
%0 Journal Article
%A E. E. Permyakova
%T Limit theorems for random processes with random time substitution
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2008
%P 49-58
%N 12
%U http://geodesic.mathdoc.fr/item/IVM_2008_12_a6/
%G ru
%F IVM_2008_12_a6

[1] Silvestrov D. S., Predelnye teoremy dlya slozhnykh sluchainykh funktsii, Vischa shkola, Kiev, 1974, 320 pp. | MR

[2] Chuprunov A., Fazekas I., “Almost sure versions of some analogues of the invariance principle”, Publicationes Math., Debrecen, 54:3 (1999), 457–471 | MR | Zbl

[3] Chuprunov A., Fazekas I., “Integral analogues of almost sure limit theorems”, Periodica Math. Hungarica, 5:1 (2005), 61–78 | DOI | MR

[4] Fazekash I., Chuprunov A. N., “Pochti navernoe predelnye teoremy dlya statistiki Pirsona”, Teor. veroyatnostei i ee prim., 48:1 (2003), 162–169 | MR

[5] Fazekas I., Chuprunov A., Convergence of random step lines to Ornstein–Uhlenbeck type processes, Technical Report of the Debrecen University, No 24, 1996, p. 22. | MR

[6] Atlagh M., Theoreme centrale limite presque sur et loi du logarithme itere, Institut de recherche mathematique avancee, Strasburg, 1996, 62 pp. | MR

[7] Stone C., “Weak convergence of stochastic processes on semiinfinite time intervals”, Proc. Amer. Math. Soc., 14 (1963), 694–696 | DOI | MR | Zbl

[8] Billingsli P., Skhodimost veroyatnostnykh mer, Nauka, M., 1977, 352 pp. | MR

[9] Bulinskii A. V., Shiryaev A. N., Teoriya sluchainykh protsessov, Fizmatlit, M., 2003, 400 pp. | MR

[10] Permiakova E., “Functional limit theorems for Levy processes and their almost-sure versions”, Liet. matem. rink., 47:1 (2007), 81–92 | MR | Zbl

[11] Chuprunov A., Fazekas I., “Almost sure versions of some functional limit theorems”, Publicationes Math., Debrecen, 2001, no. 265, 14 | MR