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Stochastic process, compatible

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adapted stochastic process

A family of random variables defined on a measurable space , with an increasing family of sub--fields , such that the are -measurable for every . In order to stress this property for such processes, one often uses the notation

or

and says that is -adapted, or adapted to the family , or that is an adapted process. Corresponding definitions can also be given in the case of discrete time, and then "adapted process" is sometimes replaced by "adapted sequence" .

References

[1] C. Dellacherie, "Capacités et processus stochastiques" , Springer (1972)


Comments

For additional references, see Stochastic process.

How to Cite This Entry:
Stochastic process, compatible. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stochastic_process,_compatible&oldid=32548
This article was adapted from an original article by A.N. Shiryaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article