Consider stochastic process ##X(t)## with properties(adsbygoogle = window.adsbygoogle || []).push({});

$$

\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?

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# Example of a non-Gaussian stochastic process?

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