Example of a non-Gaussian stochastic process?

by Jano L.
Tags: nongaussian, process, stochastic
 PF Gold P: 1,141 Consider stochastic process ##X(t)## with properties $$\langle X(t) \rangle = 0,$$ $$\langle X(t) X(t-\tau) \rangle = C_0e^{-|\tau|/\tau_c}.$$ For example, the position of a Brownian particle in harmonic potential can be described by ##X##. In that case, the probability distribution will be Gaussian, i.e. $$\frac{dp}{dX} (X) = Ae^{-\frac{|X^2|}{2\sigma^2}}$$ with some ##A, \sigma##. Do you know some example of a stochastic process ##X## with the above two properties (average value and correlation function) which however does not have Gaussian probability distribution?