Neurons live in a noisy environment; that is, they are subjected to many sources of noise. For example, we treat ion channels deterministically, but in reality, opening and closing of channels is a probablistic event. Similarly, there is spontaneous release of neurotransmitter which leads to random bombardment of small depolarizations and hyperpolarizations. In vivo, there is increasing evidence that cortical neurons live in a high-conductance state due to the asynchronous firing of the cells which are presynaptic to them. Noise in neural and other excitable systems has been the subject of research since the early 1960s. There are a number of good books and reviews about the subject. We single out the extensive review  and the books [274, 169].
KeywordsFiring Rate Stochastic Differential Equation Passage Time Wiener Process Planck Equation
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