Jason Murcko

Harvey Mudd College Mathematics 2005

Thesis Advisor: Prof. Henry A. Krieger
Second Reader: Prof. Lesley A. Ward
E-Mail: jmurcko@hmc.edu
Documents: Thesis Proposal
10-Minute Fall Presentation
20-Minute Fall Presentation
Revised Problem Statement
Annotated Bibliography
Mid-year Report
Project Days Presentation
Project Days Poster
Final Thesis

Cesaro Limits of Analytically Perturbed Stochastic Matrices

Let P(&epsilon) be an analytic perturbation of a stochastic matrix P0 which remains stochastic for all sufficiently small positive &epsilon . We investigate the hybrid Cesaro limit of P(&epsilon), focusing on extending past results of Filar, Krieger, and Syed to the case where P0 has eigenvalues on the unit circle in the complex plane other than 1. (The hybrid Cesaro limit is related to the continuity of the long-term behavior of the associated perturbed Markov chain at &epsilon = 0.)