Predictable process: Difference between revisions

Revision as of 14:16, 1 May 2013

Revision as of 14:17, 1 May 2013

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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_{t}</math> is measureablemeasurable with respect to the &sigma;-algebra <math>\mathcal{F}_{t^-}</math> for each time ''t''.<ref>{{cite web|title=Predictable processes: properties|url=http://www.math.ku.dk/~jesper/teaching/b108/slides38.pdf|format=pdf|accessdate=October 15, 2011}}</ref>

== Examples ==