The paper deals with the stochastically recursive sequences { X ( n ) } defined as the solutions of equations X ( n + 1 ) = f ( X ( n ) , Î¾n ) (where Î¾n is a given random sequence), and with randomâ€¦ (More)

In this review, we consider boundary problems for random walks generated by sums of independent items and some of their generalizations. Let 1, 42, . . * be identically distributed independent randomâ€¦ (More)

This paper is devoted to a study of the integral of the workload process of the single server queue, in particular during one busy period. Firstly, we find asymptotics of the area A swept under theâ€¦ (More)

A Markov polling system with infinitely many stations is studied. The topic is the ergodicity of the infinite-dimensional process of queue lengths. For the infinite-dimensional process, the usualâ€¦ (More)

In this paper, we consider time-homogeneous and asymptotically space-homogeneous Markov chains that take values on the real line and have an invariant measure. Such a measure always exists if theâ€¦ (More)

This paper continues investigations of [A. A. Borovkov and A. D. Korshunov, Theory Probab. Appl., 41 (1996), pp. 1â€“24]. We consider a time-homogeneous and asymptotically spacehomogeneous Markov chainâ€¦ (More)

This paper continues investigations of A. A. Borovkov and D. A. Korshunov [Theory Probab. Appl., 41 (1996), pp. 1â€“24 and 45 (2000), pp. 379â€“405]. We consider a time-homogeneous Markov chain {X(n)}â€¦ (More)