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Title: A New Class of Processes for Formalizing and Generalizing Individual-Based Models: The Semi-Semi-Markov Processes
Authors: Jacob, C.
F. Viet, A.
Keywords: Individual-Based Model
Multi-Agent Model
Random Graph
Complex System
Branching Process
Semi-Markov Process
Markov Renewal Process
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Pliska Studia Mathematica Bulgarica, Vol. 18, No 1, (2007), 121p-144p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: 60K15, 60K20, 60G20,60J75, 60J80, 60J85, 60-08, 90B15.
ISSN: 0204-9805
Appears in Collections:2007 Volume 18

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