Related papers: On Kesten's Multivariate Choquet-Deny Lemma

The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…

We first show that a continuous function f is nonnegative on a closed set $K\subseteq R^n$ if and only if (countably many) moment matrices of some signed measure $d\nu =fd\mu$ with support equal to K, are all positive semidefinite (if $K$…

We study the rate of convergence of the Markov chain on $S_n$ which starts with a random $(n-k)$-cycle for a fixed $k \geq 1$, followed by random transpositions. The convergence to the stationary distribution turns out to be of order $n$.…

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$ -- i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every…

This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…

In this paper we study the asymptotic behavior of linear processes having as innovations mean zero, square integrable functions of stationary reversible Markov chains. In doing so we shall preserve the generality of coefficients assuming…

Consider time-homogeneous discrete-time Markov chains $X$, $Y$, and $Z$ on countable state spaces, considered as stochastic processes with specified initial distributions. Suppose for maps $f$ and $g$ that $(f(X_t))_{t \ge 0}$ and…

The paper deals with the convergence properties of the products of random (row-)stochastic matrices. The limiting behavior of such products is studied from a dynamical system point of view. In particular, by appropriately defining a dynamic…

We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…

We consider continuous--time Markov kinetics with a finite number of states and a given positive equilibrium distribution P*. For an arbitrary probability distribution $P$ we study the possible right hand sides, dP/dt, of the Kolmogorov…

The equivalence of regularity of a Q-matrix with its bounded perturbations is proved and a integration by parts formula is established for the associated Feller minimal transition functions.

This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their…

Let $n>c_1\ge c_2$ and $\Sigma$ be positive integers with $n\cdot c_1\ge \Sigma \ge n\cdot c_2.$ Let $\mD=\dds{n}{\Sigma}{c_1}{c_2}$ denote the set of all degree sequences of length $n$ with the even sum $\Sigma$ and satisfying $c_1\ge…

Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are developed using perturbations. The derivation of these…

We consider the problem of characterizing entrywise functions that preserve the cone of positive definite matrices when applied to every off-diagonal element. Our results extend theorems of Schoenberg [Duke Math. J. 9], Rudin [Duke Math. J.…

We study ternary sequences associated with a multidimensional continued fraction algorithm introduced by the first author. The algorithm is defined by two matrices and we show that it is measurably isomorphic to the shift on the set…

A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to $1$. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if $d$…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

Using the renewal approach we prove exponential inequalities for additive functionals and empirical processes of ergodic Markov chains, thus obtaining counterparts of inequalities for sums of independent random variables. The inequalities…

Benjamini, Kalai and Schramm showed that a monotone function $f : \{-1,1\}^n \to \{-1,1\}$ is noise stable if and only if it is correlated with a half-space (a set of the form $\{x: \langle x, a\rangle \le b\}$). We study noise stability in…