## Stochastically recursive sequences and their generalizations (1992)

Venue: | Siberian Adv. Math |

Citations: | 40 - 11 self |

### BibTeX

@ARTICLE{Borovkov92stochasticallyrecursive,

author = {A. A. Borovkov and S. G. Foss},

title = {Stochastically recursive sequences and their generalizations},

journal = {Siberian Adv. Math},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

The paper deals with the stochastically recursive sequences { X ( n) } defined as the solutions of equations X ( n + 1) = f ( X ( n) , ξn) (where ξn is a given random sequence), and with random sequences of a more general nature, named recursive chains. For those the theorems of existence, ergodicity, stability are established, the stationary majorants are constructed. Continuous-time processes associated with ones studied here are considered as well. Key words and phrases: stochastically recursive sequence; recursive chain; generalized Markov chain; renovating event; coupling-convergence; ergodicity; stability; rate of convergence; stationary majorants; boundedness in probability; processes admitting embedded stochastically recursive sequences. CHAPTER 1.