Geodesic
Ergodic and stability theorems for a class of stochastic equations and their applications
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 2, pp. 241-262 
A. A. Borovkov. Ergodic and stability theorems for a class of stochastic equations and their applications. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 2, pp. 241-262. http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a0/
@article{TVP_1978_23_2_a0,
     author = {A. A. Borovkov},
     title = {Ergodic and stability theorems for a~class of stochastic equations and their applications},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {241--262},
     year = {1978},
     volume = {23},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a0/}
}
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Let $\{\tau_j,\infty be a vector valued stationary metrically transitive sequence and let the sequence $w_n$ (also vector valued) be defined by relations $w_{n+1}=f(w_n,\tau_n)$, $n\ge 1$. We study the conditions under which the sequence $\{w_{n+k}\colon k\ge 0\}$ converges to some stationary sequence $\{w^k\colon k\ge 0\}$ as $n\to\infty$, and the conditions, under which the latter will be stable when the variations of the governing sequence $\{\tau_j\}$ are small. Applications to many-channel queueing systems are considered.