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Stochastic basis

From Encyclopedia of Mathematics
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A complete probability space with an increasing family of sub--algebras , which satisfies the (so-called usual) conditions:

1) it must be continuous from the right, (), ;

2) it must be complete, i.e. contains all subsets from of -measure zero.

For stochastic bases, the notations or are also used.


Comments

An increasing family of (-) algebras is usually called a filtration.

How to Cite This Entry:
Stochastic basis. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stochastic_basis&oldid=48845
This article was adapted from an original article by A.N. Shiryaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article