Geodesic
Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 2, pp. 401-426

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We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general On/Off systems, Cook's model for haploinsufficiency, and a stochastic model for bacteriophage λ.

DOI : 10.1051/cocv/2010103
Classification : 49L25, 60J25, 93E20, 92C42
Keywords: viscosity solutions, pdmp, gene networks 
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     author = {Goreac, Dan},
     title = {Viability, invariance and reachability for controlled piecewise deterministic {Markov} processes associated to gene networks},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {401--426},
     publisher = {EDP-Sciences},
     volume = {18},
     number = {2},
     year = {2012},
     doi = {10.1051/cocv/2010103},
     mrnumber = {2954632},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010103/}
}
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Goreac, Dan. Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 2, pp. 401-426. doi: 10.1051/cocv/2010103

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