We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing the basic theory of stochastic hybrid systems, including various approximation schemes in the fast switching (weak noise) limit. In subsequent sections, we consider various applications of stochastic hybrid systems, including stochastic ion channels and membrane voltage fluctuations, stochastic gap junctions and diffusion in randomly switching environments, and intracellular transport in axons and dendrites. Finally, we describe recent work on phase reduction methods for stochastic hybrid limit cycle oscillators.

中文翻译：

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细胞神经科学中的随机混合系统。

我们回顾了细胞神经科学中的随机混合系统的理论和应用的最新工作。随机混合系统或分段确定性马尔可夫过程涉及某个离散空间上分段确定性微分方程和时间均质马尔可夫链之间的耦合。后者通常代表某种随机切换过程。我们首先总结一下随机混合系统的基本理论，包括在快速切换（弱噪声）极限下的各种近似方案。在随后的部分中，我们将考虑随机混合系统的各种应用，包括随机离子通道和膜电压波动，随机切换环境中的随机间隙连接和扩散以及轴突和树突中的细胞内转运。最后，