View source for Optional random process

A [[Stochastic process|stochastic process]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/o/o068/o068560/o0685601.png" /> that is measurable (as a mapping <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/o/o068/o068560/o0685602.png" />) with respect to the [[Optional sigma-algebra|optional sigma-algebra]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/o/o068/o068560/o0685603.png" />.



====Comments====
An optional random process is also called an adapted random process.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  C. Dellacherie,   "Capacités et processus stochastiques" , Springer  (1972)  pp. Chapt. 3, Sect. 2</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  H. Bauer,   "Probability theory and elements of measure theory" , Holt, Rinehart &amp; Winston  (1972)  pp. Chapt. 11  (Translated from German)</TD></TR></table>