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For small changes, the log-return $\ln \frac{S_{t_i}}{S_{t_{i-1}}}$ is close to the simple return $\frac{S_{t_i}-S_{t_{i-1}}}{S_{t_{i-1}}}$: \begin{align*} \ln \frac{S_{t_i}}{S_{t_{i-1}}} &= \ln \Big(1+ \frac{S_{t_i}-S_{t_{i-1}}} {S_{t_{i-1}}} \Big)\\ &\approx \frac{S_{t_i}-S_{t_{i-1}}}{S_{t_{i-1}}}. \end{align*} Note also that, assuming the SDE ...



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