Doob's Theorem
A theorem proved by Doob (1942) which states that any random process which is both Gaussian and Markov has the following forms for its correlation function,spectral density, and probability densities:
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
 | |  | (4) |
where
is the Mean, 
the Standard Deviation, and 
the relaxation time.
References
Doob, J. L. ``Topics in the Theory of Markov Chains.'' Trans. Amer. Math. Soc. 52, 37-64, 1942.
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- Parabolic Fixed Point
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