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.
Mots clés : viscosity solutions, pdmp, gene networks
@article{COCV_2012__18_2_401_0, 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://www.numdam.org/articles/10.1051/cocv/2010103/} }
TY - JOUR AU - Goreac, Dan TI - Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 401 EP - 426 VL - 18 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2010103/ DO - 10.1051/cocv/2010103 LA - en ID - COCV_2012__18_2_401_0 ER -
%0 Journal Article %A Goreac, Dan %T Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 401-426 %V 18 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2010103/ %R 10.1051/cocv/2010103 %G en %F COCV_2012__18_2_401_0
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. http://www.numdam.org/articles/10.1051/cocv/2010103/
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