Let $L$ be the stochastic exponential of the process $\int_0^t\frac1{X_(s)}dM(s)$, an Ito integral with respect to $M$. Is the semi martingale decomposition of $L$ just $L$? I think so, because the Ito integral is a local martingale, so therefore $L$ is a local martingale, right?
2026-04-25 02:34:07.1777084447
Is the semimartingale decomposition of an exponential process just itself?
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