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rowanc1 committed Oct 30, 2024
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6 changes: 3 additions & 3 deletions papers/sam_morley/main.md
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Expand Up @@ -539,10 +539,10 @@ RoughPy streams cache the result of log-signature queries over dyadic intervals
so they can be reused in later calculations. To compute the log-signature over
any interval $I$, we granularise at a fixed stream resolution $n$ to obtain the
interval $\tilde I = [k_1/2^n, k_2/2^n)$, and then compute
:::{math}
\mathrm{LogSig}(\tilde I) = \log\biggl(\prod\_{k=k_1}^{k_2-1}
```{math}
\mathrm{LogSig}(\tilde{I}) = \log\biggl(\prod_{k=k_1}^{k_2-1}
\exp(\mathrm{LogSig}(D_k^n))\biggr).
:::
```
The $\mathrm{LogSig}(D_k^n)$ terms on the right-hand-side are either retrieved
from the cache, or computed from the underlying source. This is essentially the
Campbell-Baker-Hausdorff formula applied to the log-signatures at the finest
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