Statistical inference on markov process of neuronal impulse sequences

To clarify the stochastic properties of the neuronal impulse sequences, we have proposed a measure of statistical dependency d _i (T=τ) and an equation ? _m of the matrices of the serial correlation coefficients. Markov properties of the interval sequences could be provided with d _i (T=τ) and ? _m , which represent the necessary and sufficient condition for the statistical dependence. A method to estimate the order of Markov process with the use of d _i (T=τ) and ? _m was found to be useful in practice. This was proved by the interval sequences of the 0-th, 1-st, and 2nd order semi-Markov process generated by computer. It was also found that the order of Markov process of neuronal impulse sequence is an important parameter representing the pattern of the sequence. This was proved with computer simulation by semi-Markov model of impulse sequence.