Estimating statistics of neuronal dynamics via Markov chains

We present an efficient computational method for estimating the mean and va riance of interspike intervals defined by the timing of spikes in typical o rbits of one-dimensional neuronal maps. This is equivalent to finding the m ean and variance of return times of orbits to particular regions of phase s pace. Rather than computing estimates directly from time series, the system is modelled as a finite state Markov chain to extract stationary behaviour in the form of invariant measures and average absorption times. Ergodic-th eoretic formulae are then applied to produce the estimates without the need to generate orbits directly. The approach may be applied to both determini stic and randomly forced systems.