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

Viability, Invariance and Reachability for Controlled Piecewise Deterministic Markov Processes Associated to Gene Networks