Further approaches to computing fundamental characteristics of birth-death processes. (English) Zbl 0995.60074
Summary: General and unifying approaches are discussed for computing fundamental characteristics of both continuous-time and discrete-time birth-death processes. In particular, an exponential family framework is used to derive explicit expressions, in terms of continued fractions, for joint generating functions of first-passage times and a whole collection of associated random quantities, and a random sum representation is used to obtain formulae for means, variances and covariances of stopped reward functions defined on a birth-death process.
MSC:
60J27 | Continuous-time Markov processes on discrete state spaces |
60J22 | Computational methods in Markov chains |
92D30 | Epidemiology |