Dynamique des populations : contrôle stochastique et modélisation hybride du cancer

Julien Claisse 1
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : The main objective of this thesis is to develop stochastic control theory and applications to population dynamics. From a theoritical point of view, we study finite horizon stochastic control problems on diffusion processes, nonlinear branching processes and branching diffusion processes. In each case we establish a dynamic programmic principle by carefully proving a conditioning argument similar to the strong Markov property for controlled processes. Then we deduce that the value function is a (viscosity or regular) solution of the associated Hamilton-Jacobi-Bellman equation. In the regular case, we further identify an optimal control in the class of markovian strategies thanks to a verification theorem. From a pratical point of view, we are interested in mathematical modelling of cancer growth and treatment. More precisely, we build a hybrid model of tumor growth taking into account the essential role of acidity. Therapeutic targets appear explicitly as model parameters in order to be able to evaluate treatment strategies.
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Julien Claisse. Dynamique des populations : contrôle stochastique et modélisation hybride du cancer. Mathématiques générales [math.GM]. Université Nice Sophia Antipolis, 2014. Français. ⟨NNT : 2014NICE4049⟩. ⟨tel-01066020⟩



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