  We propose a correlated stochastic process of which the novel non-Gaussian
probability mass function is constructed by exactly solving moment generating
function. The calculation of cumulants and auto-correlation shows that the
process is convergent and scale invariant in the large but finite number limit.
We demonstrate that the model consistently explains both the distribution and
the correlation of discrete financial time-series data, and predicts the data
distribution with high precision in the small number regime.
