A

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- Jun 4th 2010, 08:52 AMHansGMartingales
A

- Jun 4th 2010, 10:12 AMLaurent
- Jun 5th 2010, 02:14 AMHansG
B

- Jun 7th 2010, 02:29 PMLaurent
Once you get , you are done proving that is a local martingale, whatever the right-continuous adapted process is. You don't have to specify that is a martingale or some kind of product of martingales.

As for proving that are true martingales, you have the following result: if is a local martingale with , the following is equivalent :

(i) is a true square-integrable martingale ( )

(ii) for all , .

Remember that so that you can easily check this criterion in your case.