Matrix Analysis for Continuous-Time Markov Chains

Abstract

Continuous-time Markov chains have transition matrices that vary continuously in time. Classical theory of nonnegative matrices, M-matrices and matrix exponentials is used in the literature to study their dynamics, probability distributions and other stochastic properties. For the benefit of Perron-Frobenius cognoscentes, this theory is surveyed and further adapted to study continuous-time Markov chains on finite state spaces.

Keywords

• continuous-time markov chain
• stochastic matrix
• m-matrix
• matrix exponential
• exponential nonnegativity
• irreducible matrix
• primitive matrix
• group inverse
• 15b51
• 15a48
• 15a18
• 15a09
• 60j10
• 92d40