Let be a standard 2-D Brownian motion, and is an adapted process satisfying, for some constants
Let be a martingale of
[Q.] Does there exist 1-1 mapping such that
where and are finite variation and martingale terms associated to Doob’s decomposition of ?
In some special cases, the answer is positive. For instance, if for some deterministic function satisfying
then one can check by Ito’s formula
is homeomorphism satisfying the requirement.