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	Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model
	Ding, Shaojie ; Qian, Min ; Qian, Hong ; Zhang, Xuejuan
	2016
关键词	CHEMICALLY REACTING SYSTEMS CHANNEL FLUCTUATIONS ACTION-POTENTIALS KINETICS MEMBRANE ALGORITHM EQUATIONS DYNAMICS
英文摘要	The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented. Published by AIP Publishing.; National Natural Science Foundation of China [10971196, 61271396]; Excellent Youth Foundation of Zhejiang Scientific Committee [LR13A05000]; China Scholarship Council; SCI(E); ARTICLE; hqian@u.washington.edu; xuejuanzhang@gmail.com; 24; 145
语种	英语
出处	SCI
出版者	JOURNAL OF CHEMICAL PHYSICS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/457966]
专题	数学科学学院
推荐引用方式 GB/T 7714	Ding, Shaojie,Qian, Min,Qian, Hong,et al. Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model. 2016-01-01.

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