Jump Markov processes

By associating types with the decisions or choices, we may think of groups in which each agent has several alternative decisions to choose from. Agents may change their types when types are associated with their decisions, actions, or choices. In open models, agents of various types may, in addition, enter or leave the group or collection. These changes of fractions may occur at any time, not necessarily at the equally spaced discrete points of discrete dynamics. They are therefore modeled by continous-time (jump) Markov processes with finite or countable state spaces. See Norris (1997).

Among Markov processes we use those with a finite or at most countable states, and time running continuously They are called jump or pure jump Markov processes in the probability literature.

1.4