Stationary Markov chains with linear regressions

Stationary Markov chains with linear regressions

In Bryc(1998) we determined one dimensional distributions of a stationary field with linear regressions (1) and quadratic conditional variances (2) under a linear constraint (7) on the coefficients of the quadratic expression (3). In this paper we show that for stationary Markov chains with linear regressions and quadratic conditional variances the coefficients of the quadratic expression are i...

Stationary random fields with linear regressions ∗

We analyze and identify stationary fields with linear regressions and quadratic conditional variances. We give sufficient conditions to determine one dimensional distributions uniquely as normal, and as certain compactly-supported distributions. Our technique relies on orthogonal polynomials, which under our assumptions turn out to be a version of the so called continuous q-Hermite polynomials.

Stopped Markov chains with stationary occupation times

Let E be a nite set equipped with a group G of bijective transformations and suppose that X is an irreducible Markov chain on E that is equivariant under the action of G. In particular, if E = G with the corresponding transformations being left or right multiplication, then X is a random walk on G. We show that when X is started at a xed point there is a stopping time U such that the distributi...

Transient Markov Chains with Stationary Measures

Stationary Probabilities of Markov Chains

In this paper, based on probabilistic arguments, we obtain an explicit solution of the stationary distribution for a discrete time Markov chain with an upper Hessenberg time stationary transition probability matrix. Our solution then leads to a numerically stable and eecient algorithm for computing stationary probabilities. Two other expressions for the stationary distribution are also derived,...