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Infection Time in Multi-Stable Gene Networks. A BSVI With Non-Convex, Switch-Dependent Reflection Model

Dan Goreac 1 Eduard Rotenstein 2
1 PS
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : 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 (of PDMP type) and is reflected in some mode-dependent non-convex domains. First, we study the existence of solution to these backward stochastic variational inclusions (BSVI) by reducing them 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) BSVI in a family of regular measures. Regularity, support and structure properties of these sets are given.
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Preprints, Working Papers, ...
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https://hal-upec-upem.archives-ouvertes.fr/hal-01211101
Contributor : Dan Goreac <>
Submitted on : Saturday, October 3, 2015 - 1:43:36 AM
Last modification on : Thursday, March 19, 2020 - 12:26:03 PM
Long-term archiving on: : Monday, January 4, 2016 - 10:11:35 AM

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  • HAL Id : hal-01211101, version 1

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Dan Goreac, Eduard Rotenstein. Infection Time in Multi-Stable Gene Networks. A BSVI With Non-Convex, Switch-Dependent Reflection Model. 2015. ⟨hal-01211101v1⟩

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