Stochastically recursive sequences and their generalizations

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.