Let $(X_t)$ be a continuous stochastic process and $g$ a function such that $g(t,X_t)$ is a martingale with regard to $(X_t)$. Does that mean anything for $X_t$ ? Would that make $(X_t)$ a semimartingale for example ?
2026-04-12 17:07:13.1776013633
If $g(t,X_t)$ is a martingale, is $X_t$ a semimartingale?
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