Variation of the Response functions in stochastic spiking neuron model

In this report, we theoretically examine the responses of spiking neurons to spike sequences which obey an inhomogeneous Poisson process. When statistically independent random inputs are provided, the probability densities of membrane potential converge to Gaussian distribution. In this case, the stochastic process of the membrane potential becomes Gauss process. We introduce a calculation method which can precisely obtain the dynamics of the membrane potential and the firing probability. We find that the synaptic time constant s has significant effect on the firing probability, although it is often ignored in stochasic process studies. key words Temporal coding, Spiking neurons, Poisson process, Gauss process, Markov process, Firing probability, Synaptic time constant.