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.

© 1996-9

1999-05-24