Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 529-541
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E. I. Kaplan; D. S. Sil'vestrov. The invariance principle type theorems for recurrent semi-Markov processes with a general state space. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 529-541. http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a6/
@article{TVP_1979_24_3_a6,
author = {E. I. Kaplan and D. S. Sil'vestrov},
title = {The invariance principle type theorems for recurrent {semi-Markov} processes with a~general state space},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {529--541},
year = {1979},
volume = {24},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a6/}
}
TY - JOUR
AU - E. I. Kaplan
AU - D. S. Sil'vestrov
TI - The invariance principle type theorems for recurrent semi-Markov processes with a general state space
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1979
SP - 529
EP - 541
VL - 24
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a6/
LA - ru
ID - TVP_1979_24_3_a6
ER -
%0 Journal Article
%A E. I. Kaplan
%A D. S. Sil'vestrov
%T The invariance principle type theorems for recurrent semi-Markov processes with a general state space
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1979
%P 529-541
%V 24
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a6/
%G ru
%F TVP_1979_24_3_a6
The invariance principle type theorems for processes of sums of random variables defined on a recurrent semi-Markov process with a general state space are proved. The results are obtained in assumption that for a fixed subset of state space the recurrent times have a stable limit distribution $L_\alpha$, $\alpha\in(0,1]$ (the case $\alpha=1$ corresponds to the ergodic process).
