A random walk is a sequence {Sn, n≥ 0} of random variables with independent, identically
distributed (iid) increments {Xk, k≥ 1} and S0= 0. A Bernoulli random walk (also called a …

In this paper, we study the problems of sequential probability ratio tests for parameterized
hidden Markov models. We investigate in some detail the performance of the tests and …

We consider the asymptotic behaviour of the stationary tail probabilities in the discrete-time
GI/G/1-type queue with countable background state space. These probabilities are …

We consider the stationary distribution of the M/GI/1 type queue when background states are
countable. We are interested in its tail behavior. To this end, we derive a Markov renewal …

Let X n, n≥ 0 be a Markov chain on a general state space X with transition probability P and
stationary probability π. Suppose an additive component S n takes values in the real line R …

We prove precise stability results for overshoots of Markov additive processes (MAPs) with
finite modulating space. Our approach is based on the Markovian nature of overshoots of …

Let 𝓈 be a finite or countable set. Given a matrix F=(Fij) i, j∈ 𝓈 of distribution functions on R
and a quasistochastic matrix Q=(qij) i, j∈ 𝓈, ie an irreducible nonnegative matrix with …

The paper is a sketch of systematic presentation of distributional limit theorems and their
refinements for compound sums. When analyzing, eg, ergodic semi-Markov systems with …

Let (U, d) be a complete separable metric space and (F n) n≥ 0 a sequence of random
functions from U to U. Motivated by studying the stability property for Markovian dynamic …

We consider local alignments without gaps of two independent Markov chains from a finite
alphabet, and we derive sufficient conditions for the number of essentially different local …