Stochastic process, compatible

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.