Absolutely-unbiased sequence
A sequence of random variables for which the conditions
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are fulfilled, for . The partial sums
of an absolutely-unbiased sequence form a martingale. These two types of sequences are interconnected as follows: The sequence
forms a martingale if and only if it is of the form
(
and
is a constant), where
is an absolutely-unbiased sequence. Thus, all martingales are related to partial sums of certain absolutely-unbiased sequences. Simple examples of absolutely-unbiased sequences are sequences of independent random variables with mathematical expectation zero. Besides the term "unbiased" the term "fair" — with the related concept of a "fair play" , is also employed.
Comments
In [a1] the term "absolutely fair sequenceabsolutely fair" is used instead of absolutely-unbiased.
References
[a1] | W. Feller, "An introduction to probability theory and its applications" , 2 , Wiley (1966) pp. 210 |
Absolutely-unbiased sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Absolutely-unbiased_sequence&oldid=25932