Difference between revisions of "Optional random process"
From Encyclopedia of Mathematics
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| − | A [[ | + | A [[stochastic process]] $X = (X_t(\omega),F_t)_{t\ge0}$ that is [[measurable mapping|measurable]] (as a mapping $(\omega,t) \mapsto X(\omega,t) = X_t(\omega)$) with respect to the [[optional sigma-algebra]] $\mathcal{O} = \mathcal{O}(\mathbf{F})$. |
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====References==== | ====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 & Winston (1972) pp. Chapt. 11 (Translated from German)</TD></TR></table> | + | <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 & Winston (1972) pp. Chapt. 11 (Translated from German)</TD></TR> | ||
| + | </table> | ||
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| + | {{TEX|done}} | ||
Latest revision as of 20:27, 1 October 2016
A stochastic process $X = (X_t(\omega),F_t)_{t\ge0}$ that is measurable (as a mapping $(\omega,t) \mapsto X(\omega,t) = X_t(\omega)$) with respect to the optional sigma-algebra $\mathcal{O} = \mathcal{O}(\mathbf{F})$.
Comments
An optional random process is also called an adapted random process.
References
| [a1] | C. Dellacherie, "Capacités et processus stochastiques" , Springer (1972) pp. Chapt. 3, Sect. 2 |
| [a2] | H. Bauer, "Probability theory and elements of measure theory" , Holt, Rinehart & Winston (1972) pp. Chapt. 11 (Translated from German) |
How to Cite This Entry:
Optional random process. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Optional_random_process&oldid=39349
Optional random process. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Optional_random_process&oldid=39349
This article was adapted from an original article by A.N. Shiryaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article