Let $X$ be a semimartingale (sum of local martingale and finite variation process) and let $T$ be a non-decreasing process. Is it true that process $X_{T_t}$ is a semimartingale?
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Let $X$ be a semimartingale (sum of local martingale and finite variation process) and let $T$ be a non-decreasing process. Is it true that process $X_{T_t}$ is a semimartingale?