Trajectory composition of Poisson time changes and Markov counting systems

Abstract

Changing time of simple continuous-time Markov counting processes by independent unit-rate Poisson processes results in Markov counting processes for which we provide closed-form transition rates via composition of trajectories and with which we construct novel, simpler infinitesimally over-dispersed processes.

9 pages, 1 figure

References in corpus (3)

• Time series analysis via mechanistic models
• Time-Changed Poisson Processes
• Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems