Doob,s Theorem
المؤلف:
Finch, S
المصدر:
"Ornstein-Uhlenbeck Process." May 15, 2004. https://algo.inria.fr/csolve/ou.pdf.
الجزء والصفحة:
...
4-4-2021
2004
Doob's Theorem
A theorem proved by Doob (1942) which states that any random process which is both normal and Markov has the following forms for its correlation function 
, spectral density 
, and probability densities 
and 
:
where 
is the mean, 
the standard deviation, and 
the relaxation time.
REFERENCES:
Doob, J. L. "The Brownian Movement and Stochastic Equations." Ann. Math. 43, 351-369, 1942. Reprinted in Selected Papers on Noise and Stochastic Processes (Ed. N. Wax). New York: Dover, pp. 319-337, 1954.
Finch, S. "Ornstein-Uhlenbeck Process." May 15, 2004. https://algo.inria.fr/csolve/ou.pdf.
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