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Absolutely-unbiased sequence

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A sequence of random variables for which the conditions

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
How to Cite This Entry:
Absolutely-unbiased sequence. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Absolutely-unbiased_sequence&oldid=25932
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article