An exactly solvable correlated stochastic process in finite time

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 time limit. We demonstrate that the model infers the correlation strength in a discrete correlated time-series data, and predicts the data distribution with high precision in the finite time regime.