- Let be $X=M+A$ a semimartingale with $M$ being a local martingale and $A$ an adapted process a finite variation. If $M$ and $A$ are bounded, then of course $X$ is bounded as well. Is the converse true? Do you have a counterexample?
- If not, provided $X$ and $[X]$ are bounded, can we conclude $M$ and $A$ to be bounded? Or is there again a counterexample?
2026-02-23 06:20:57.1771827657
$X=M+A$ bounded semimartingale, then $M$ and $A$ are bounded? Counterexample?
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