Rootfinding for Markov Chains with Quasi-Triangular Transition Matrices
Abstract
Numerical rootfinding problems are quite common in stochastic modeling. However, many solutions stop at the presentation of a probability generating function for the state probabilities. But with increasing easy access to computing power, many problems whose answers were typically left in incomplete form or for which there has been a search for alternative solution methods are currently being reexamined. The class of Markov chains with quasi- triangular layouts (i.e., those having sub- or super-triangular sets of zeros) are good case in point. They have an especially nice structure which leads to a rather concise representation for the generating functions. But the complete solution then requires the finding of roots. Fortunately, these problems can be shown to have special properties that make accurate rootfinding quite feasible. In this paper, we show that the roots of the critical equations for these models are indeed unique and located in known regions in the complex plane. Keywords: Applied probability; Computational analysis; Computational probability; Markov chains; Numerical methods; Probability; Rootfinding; Stochastic models.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 31, 1988
- Accession Number
- ADA202468
Entities
People
- Carl M. Harris
Organizations
- George Mason University