Difference between revisions of "Predictable random process"
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A [[Stochastic process|stochastic process]] $X=(X_t(\omega),\mathcal F_t)$ that is measurable (as a mapping $(\omega,t)\to X(\omega,t)=X_t(\omega)$) with respect to the [[Predictable sigma-algebra|predictable sigma-algebra]] $\mathcal P=\mathcal P(\mathbf F)$, where $\mathbf F=(\mathcal F_t)_t$. | A [[Stochastic process|stochastic process]] $X=(X_t(\omega),\mathcal F_t)$ that is measurable (as a mapping $(\omega,t)\to X(\omega,t)=X_t(\omega)$) with respect to the [[Predictable sigma-algebra|predictable sigma-algebra]] $\mathcal P=\mathcal P(\mathbf F)$, where $\mathbf F=(\mathcal F_t)_t$. | ||
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====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> C. Dellacherie, P.A. Meyer, "Probabilities and potential" , '''B''' , North-Holland (1982) (Translated from French)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> R.S. Liptser, A.N. Shiryaev, "Statistics of random processes" , '''II''' , Springer (1978) pp. 301ff (Translated from Russian)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> R.Sh. Liptser, A.N. [A.N. Shiryaev] Shiryayev, "Theory of martingales" , Kluwer (1989) (Translated from Russian)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> C. Dellacherie, P.A. Meyer, "Probabilities and potential" , '''B''' , North-Holland (1982) (Translated from French)</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> R.S. Liptser, A.N. Shiryaev, "Statistics of random processes" , '''II''' , Springer (1978) pp. 301ff (Translated from Russian)</TD></TR> | ||
| + | <TR><TD valign="top">[a3]</TD> <TD valign="top"> R.Sh. Liptser, A.N. [A.N. Shiryaev] Shiryayev, "Theory of martingales" , Kluwer (1989) (Translated from Russian)</TD></TR> | ||
| + | </table> | ||
Latest revision as of 14:08, 15 April 2023
A stochastic process $X=(X_t(\omega),\mathcal F_t)$ that is measurable (as a mapping $(\omega,t)\to X(\omega,t)=X_t(\omega)$) with respect to the predictable sigma-algebra $\mathcal P=\mathcal P(\mathbf F)$, where $\mathbf F=(\mathcal F_t)_t$.
References
| [a1] | C. Dellacherie, P.A. Meyer, "Probabilities and potential" , B , North-Holland (1982) (Translated from French) |
| [a2] | R.S. Liptser, A.N. Shiryaev, "Statistics of random processes" , II , Springer (1978) pp. 301ff (Translated from Russian) |
| [a3] | R.Sh. Liptser, A.N. [A.N. Shiryaev] Shiryayev, "Theory of martingales" , Kluwer (1989) (Translated from Russian) |
How to Cite This Entry:
Predictable random process. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Predictable_random_process&oldid=53795
Predictable random process. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Predictable_random_process&oldid=53795
This article was adapted from an original article by A.N. Shiryaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article