Infection Time in Multistable Gene Networks. A Backward Stochastic Variational Inequality with Nonconvex Switch-Dependent Reflection Approach - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Set-Valued and Variational Analysis Année : 2016

Infection Time in Multistable Gene Networks. A Backward Stochastic Variational Inequality with Nonconvex Switch-Dependent Reflection Approach

Résumé

We investigate a mathematical model associated to the infection time in multistable gene networks. The mathematical processes are of hybrid switch type. The switch is governed by pure jump modes and linked to DNA bindings. The differential component follows backward stochastic dynamics reflected in some mode-dependent nonconvex domains. First, we study the existence of solutions to the resulting stochastic variational inclusions, by reducing the model to a family of ordinary variational inclusions with generalized reflection in semiconvex domains. Second, by considering control-dependent drivers, we hint to some model-selection approach by embedding the controlled backward stochastic variational inclusion in a family of regular measures. Regularity and structural properties of these sets are given.
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Dates et versions

hal-01211101 , version 1 (03-10-2015)
hal-01211101 , version 2 (04-09-2016)

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Citer

Dan Goreac, Eduard Rotenstein. Infection Time in Multistable Gene Networks. A Backward Stochastic Variational Inequality with Nonconvex Switch-Dependent Reflection Approach. Set-Valued and Variational Analysis, 2016, ⟨10.1007/s11228-016-0382-7⟩. ⟨hal-01211101v2⟩
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