The least -algebra of sets in
generated by all mappings of the set into that are (for each fixed ) continuous from the left (in ) and -adapted to a non-decreasing family of sub--algebras , , where is a measurable space. A predictable -algebra can be generated by any of the following families of sets:
2) , where , and , where and .
Between optional -algebras (cf. Optional sigma-algebra) and predictable -algebras there is the relation .
|||C. Dellacherie, "Capacités et processus stochastique" , Springer (1972)|
Instead of "(s-) algebra" one more often uses (-) field.
|[a1]||C. Dellacherie, P.A. Meyer, "Probabilities and potential" , A-C , North-Holland (1978–1988) (Translated from French)|
Predictable sigma-algebra. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Predictable_sigma-algebra&oldid=39353