On eigenvalue bounds for the finite-state birth-death process intensity matrix

Calculating bounds on expected return and first passage times in finite-state imprecise birth-death chains

We provide simple methods for computing exact bounds on expected return and first passage times in finite-state birth-death chains, when the transition probabilities are imprecise, in the sense that they are only known to belong to convex closed sets of probability mass functions. We describe a precise birth-death chain and then we define an imprecise version of it. We present the main results ...

The decay parameter and the smallest Dirichlet eigenvalue of a birth-death process

Software for computing eigenvalue bounds for iterative subspace matrix methods

A procedure is presented for the computation of bounds to eigenvalues of the generalized hermitian eigenvalue problem and to the standard hermitian eigenvalue problem. This procedure is applicable to iterative subspace eigenvalue methods and to both outer and inner eigenvalues. The Ritz values and their corresponding residual norms, all of which are computable quantities, are needed by the proc...

A general theory on spectral properties of state-homogeneous finite-state quasi-birth-death processes

In this paper a spectral theory pertaining to Quasi-Birth-Death Processes (QBDs) is presented. The QBD, which is a generalization of the BirthDeath Process, is a powerful tool that can be utilized in modeling many stochastic phenomena. Our theory is based on the application of a matrix polynomial method to obtain the steady-state probabilities in state-homogeneous finite-state QBDs. The method ...

Exact Transient Solution of a State-dependent Birth-death Process

Continued fractions (CFs) play a fundamental role in many investigations due to its applications to diverse fields like number theory, special functions, approximations, moment problems, digital networks, statistics, and signal processing. Their importance has grown further with the advent of fast computing facilities. The problem of converting a continued fraction into a power series is import...