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Communication dans un congrès

Semi-semi-Markov processes : a new class of processes for formalizing and generalizing state-dependent individual-based models

Abstract : Individual-based models are a “bottom-up” approach for calculating empirical distributions at the level of the population from simulated individual trajecto- ries. 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. The starting point of this work was the modelling of the propagation of a disease (stochastic process) in a branching population with interactions (nonbounded random graph).
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Communication dans un congrès
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https://hal.inrae.fr/hal-02822679
Déposant : Migration Prodinra <>
Soumis le : samedi 6 juin 2020 - 20:39:27
Dernière modification le : vendredi 12 juin 2020 - 10:43:26

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  • HAL Id : hal-02822679, version 1
  • PRODINRA : 43842

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Christine Jacob, Anne France Viet. Semi-semi-Markov processes : a new class of processes for formalizing and generalizing state-dependent individual-based models. Workshop on Stochastic Modelling in Population Dynamics, Apr 2007, Luminy, France. 24 p. ⟨hal-02822679⟩

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