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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 $\mathbf F=(\mathcal F_t)_t$.
 
 
 
====Comments====
 
 
  
 
====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>
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<table>
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<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>
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</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=32606
This article was adapted from an original article by A.N. Shiryaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article