Stochastic basis
From Encyclopedia of Mathematics
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
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