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Is there an example of progressively measurable process that is not predictable?

This question is motivated by Revuz-Yor, Continuous Martingales and Brownian Motion http://www.springer.com/gb/book/9783540643258, where they define the space of integrands with respect to a continuous $L^2$-bounded martingale $M$ as the progressively measurable processes $\phi$ such that $$\int_0^\infty \phi^2d<M<\infty$$

So they ask $\phi$ to be progressively measurable instead of the very usual, stronger, hypothesis of $\phi$ being predictable.  ${}{}$ I wonder whether this space is actually bigger than the one we get with the predictability imposition, or if this yields the same result in this case.

Is there an example of progressively measurable process that is not predictable?

This question is motivated by Revuz-Yor, Continuous Martingales and Brownian Motion http://www.springer.com/gb/book/9783540643258.

They define the space of integrands with respect to a continuous $L^2$-bounded martingale $M$ as the progressively measurable processes $\phi$ such that:

$$\int_0^\infty \phi^2 dM<\infty$$

So they ask $\phi$ to be progressively measurable instead of the very usual, stronger, hypothesis of $\phi$ being predictable. 

${}{}$ I wonder whether this space is actually bigger than the one we get with the predictability imposition, or if this yields the same result in this case.

Is there an example of progressively measurable process that is not predictable?

This question is motivated by Revuz-Yor, Continuous Martingales and Brownian Motion http://www.springer.com/gb/book/9783540643258, where they define the space of integrands with respect to a continuous $L^2$-bounded martingale $M$ as the progressively measurable processes $\phi$ such that $\int_0^\infty \phi^2d<M><\infty$. So they ask $\phi$ to be progressively measurable instead of the very usual, stronger, hypothesis of $\phi$ being predictable.

I wonder whether this space is actually bigger than the one we get with the predictability imposition, or if this yields the same result in this case.

Is there an example of progressively measurable process that is not predictable?

This question is motivated by Revuz-Yor, Continuous Martingales and Brownian Motion http://www.springer.com/gb/book/9783540643258, where they define the space of integrands with respect to a continuous $L^2$-bounded martingale $M$ as the progressively measurable processes $\phi$ such that $$\int_0^\infty \phi^2d<M<\infty$$

So they ask $\phi$ to be progressively measurable instead of the very usual, stronger, hypothesis of $\phi$ being predictable. ${}{}$ I wonder whether this space is actually bigger than the one we get with the predictability imposition, or if this yields the same result in this case.

Could someone give me such an example?

The question that originally motivated this is actually the following: In Revuz-Yor, "Continuous martingales and Brownian Motion" http://www.springer.com/gb/book/9783540643258 they define the space of integrands with respect to a continuous $L^2$-bounded martingale $M$ as the progressively measurable processes $\phi$ such that $\int_0^\infty \phi^2d<M><\infty$. So they ask $\phi$ to be progressively measurable instead of the very usual, stronger, hypothesis of $\phi$ being predictable. I wonder whether this space is actually bigger to the one we get with the predictability imposition or if this yields the same result in this case.

Is there an example of progressively measurable process that is not predictable?

This question is motivated by Revuz-Yor, Continuous Martingales and Brownian Motion http://www.springer.com/gb/book/9783540643258, where they define the space of integrands with respect to a continuous $L^2$-bounded martingale $M$ as the progressively measurable processes $\phi$ such that $\int_0^\infty \phi^2d<M><\infty$. So they ask $\phi$ to be progressively measurable instead of the very usual, stronger, hypothesis of $\phi$ being predictable. 

I wonder whether this space is actually bigger than the one we get with the predictability imposition, or if this yields the same result in this case.