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Results tagged with rough-paths
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user 173490
Questions about an area of probability theory, rough paths.
4
votes
1
answer
199
views
How much can you improve a Hölder function by composing it with another?
Let $f: [0, 1] \to \mathbb R$ be a continuous function. Define the local Hölder exponent $H(f, x)$ of $f$ at $x \in [0, 1]$ by
$$H(f, x) := \sup\left\{0 \leq \alpha \leq 1\mid\lim_{\delta \to 0_+} \su …
- 6,155
3
votes
1
answer
236
views
Can any function in $C^\alpha$ be approximated in $C^{\alpha^-}$ by singular functions?
For every positive $\alpha < 1$, we consider the space $C^{\alpha}$ of Holder continuous functions of order $\alpha$ on $[0, 1]$, equipped with the norm
$$\|f\|_{C^\alpha} := \sup|f| + \sup_{x, y \in …
- 6,155