We consider the class of simple random walks or birth and death chains on the nonnegative integers. The set of return probabilities Pn00, n [greater-or-equal, slanted] 0, uniquely determines the spectral measure of the process. We characterize the class of simple random walks with the same...

In this paper we study the connection between matrix measures and random walks with a tridiagonal block transition matrix. We derive sufficient conditions such that the blocks of the n-step transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued...

A geometric approach to quadrature formulas for matrix measures is presented using the relations between the representations of the boundary points of the moment space (generated by all matrix measures) and quadrature formulas. Simple proofs of existence and uniqueness of quadrature formulas of...

In this note a matrix version of the q-d algorithm is introduced. It is shown that the algorithm may be used to obtain the coeÆcients of the recurrence relations for matrix orthogonal polynomials on the interval [0,∞) and [0;1] from its moment generating functional. The algorithm is...