基因网络中受控分段确定马尔可夫过程的生存性、不变性和可达性
Viability, Invariance and Reachability for Controlled Piecewise Deterministic Markov Processes Associated to Gene Networks
摘要：
我们的目的是描述受控分段确定性马尔可夫过程（PDMP）的生存能力，不变性和一些可达性的性质。利用黏性解理论的分析方法，我们建立了关于一阶法锥的生存性和不变性的判据。我们还研究了任意开集的可达性。该方法是基于粘性技术和对偶一些相关的线性化问题。理论结果被应用到一般的开/关系统，库克的模型为haploinssufficiency，和噬菌体λ的随机模型。
英文摘要：
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 haploinssuficiency, and a stochastic model for bacteriophage lambda.
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