Predictable process: Difference between revisions

Revision as of 14:55, 11 September 2014

Revision as of 14:15, 15 September 2014

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=== Continuous-time process ===

Given a filtered probability space <math>(\Omega,\mathcal{F},(\mathcal{F}_t)_{t \geq 0},\mathbb{P})</math>, then a [[continuous-time stochastic process]] <math>(X_t)_{t \geq 0}</math> is ''predictable'' if <math>X</math>, considered as a mapping from <math>\Omega \times \mathbb{R}_{+} </math>, is measurable with respect to the &sigma;-algebra generated by all left-continuous adapted processes.<ref>{{cite web|title=Predictable processes: properties|url=http://www.math.ku.dk/~jesper/teaching/b108/slides38.pdf|format=pdf|accessdate=October 15, 2011}}{{Dead link}}</ref>

== Examples ==

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== References ==

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