ABSTRACT
A natural generalization of the Markov chain in discrete time is to allow the times between transitions to be continuous random variables. The motivating example concerns multiplicative showers of cosmic radiation. The difference between deterministic and stochastic models is illustrated using linear and nonlinear birth processes. The relation to the previous chapter is brought out in the discrete skeleton and the jump chain. Some queueing models are presented, and the statistical inference for both nonparametric and parametric models of continuous time Markov processes is discussed. Partially observed processes are used to model the activity of synaptic nerve cells. The blood production in cats is described using a hidden Markov process.
