Set-Valued and Variational Analysis

, Volume 24, Issue 4, pp 707–734 | Cite as

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

  • Dan GoreacEmail author
  • Eduard Rotenstein


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.


Backward stochastic variational inclusion Nonconvex domains Piecewise Deterministic Markov Processes (PDMP) Occupation measures 

Mathematics Subject Classification (2010)

60H10 60G55 60J75 92C42 93E03 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.LAMA (UMR 8050), UPEMLV, UPEC, CNRSUniversité Paris-EstMarne-la-ValléeFrance
  2. 2.Faculty of Mathematics“Alexandru Ioan Cuza” UniversityIasiRomania

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