Individual-Based Model Multi-Agent Model Random Graph Complex System Branching Process Semi-Markov Process Markov Renewal Process
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 18, No 1, (2007), 121p-144p
Individual-based models are a \bottom-up" approach for calculating empirical distributions at the level of the population from simulated individual trajectories. We build a new class of stochastic processes for mathematically formalizing and generalizing these simulation models according to a \top-down" approach, when the individual state changes occur at countable random times. We allow individual population-dependent semi-Markovian transitions in a non closed population such as a branching population. These new processes are called Semi-Semi-Markov Processes (SSMP) and are generalizations of Semi-Markov processes. We calculate their kernel and their probability law, and we build a simulation algorithm from the kernel.