I’m not sure what the sufficient condition would be. Consider the case where M and N are independent standard Brownian motions. Then, taking quadratic variations, if we have and, hence . However, L is not 0.

]]>Thanks,

Alex

This was under the condition that . Integrate with respect to this, or use the fact that it implies almost everywhere under the measure.

]]>Sorry, typo.

which we can apply Theorem 2 to to show (2) holds. *

]]>Given an integrable Z, we can define a uniformly integrable martingale which we can apply Theorem to to show (2) holds.

Note that this argument is not circular – we never needed to show (2) holds for all integrable random variables to prove Theorem 2, just for the ones of the special exponential form given by (3).

]]>Yes. But — if {*F _{t}*}