Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 2, page 401-426
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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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 18.2 (2012): 401-426. <http://eudml.org/doc/277821>.

@article{Goreac2012,
abstract = {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. },
author = {Goreac, Dan},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Viscosity solutions; PDMP; gene networks; viscosity solutions; piecewise deterministic Markov processes (PDMP)},
language = {eng},
month = {7},
number = {2},
pages = {401-426},
publisher = {EDP Sciences},
title = {Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks},
url = {http://eudml.org/doc/277821},
volume = {18},
year = {2012},
}

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
DA - 2012/7//
PB - EDP Sciences
VL - 18
IS - 2
SP - 401
EP - 426
AB - 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.
LA - eng
KW - Viscosity solutions; PDMP; gene networks; viscosity solutions; piecewise deterministic Markov processes (PDMP)
UR - http://eudml.org/doc/277821
ER -

References

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