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An ergodic theorem and its generalization

✍ Scribed by Alfred A. Wolf

Publisher: Elsevier Science
Year: 1967
Tongue: English
Weight: 801 KB
Volume: 283
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(67)90044-0

No coin nor oath required. For personal study only.

✦ Synopsis

A generalized ergo& theorem is proven for a class of statirmary random processes. According lo this theorem a strictly stationary random process with finite mean, m, and variance uz2 is strictly ergo& with probabilit~e if limr+,,Rz(r) = mz2 is sdi.s+d where R*(r) is the probability cornelation function of the process. In addition to the theorem four lemmas are proven. According to these lemmas, linear operations on ergo& processes are themselves ergo&, zero-memory nonlinear operations on ergo&c processes are ergo&c, and linear combinations of wgodic processee are ergo&c. Implied from these lemmas is the result that both separable and nonseparable nonlinear operations on ergo& processes are ergo&c.

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