The text book I’m working on considers the following SDE: $dX(t) = \mu(t)dt + \sigma(t)dW(t)$, where $\mu$ is defined to be a càdlàg predictable and finite variation process, while $\sigma$ is a square integrable, predictable, non-decreasing process. Then it rules out the possibility of any jump in the process $X$. Is it correct to conclude that the process $\mu$ is continuous and hence has finite quadratic variation?



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