# Tag Info

Accepted

### What does the group action of a rough path in a Lie group look like?

Though I like the Arnoldian spirit of the question ("a group is not some set with a forgettable system of axioms but something which acts on a space"), I think the comments given above are already ...
• 2,063
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### Truncated fixed point and regularity structures

Before I try to answer the broader question let me try to clear up a potential confusion. The truncations that appear at the level of modelled distributions don't really change the distribution they ...
• 231
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### Intuition behind Gubinelli derivative

In a way it is very much like a usual derivative. Recall first that for a regular function $Y$, its derivative $Y'_s$ at a point $s$ is the (unique) number such that $$Y_{t,s}=Y'_s(t-s)+ R_{s,t},$$ ...
• 458
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### Under what condition we get back path from signatures in rough path theory?

Loops don't get canceled out in the signature. (You might like to compute the signature of a circle. The second iterated integral is nonzero; in fact, by Green's theorem, it gives you the area inside ...
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### Why the term "geometric" rough path?

I agree with Martin's answer - but there were other additional and compelling reasons. A rough path (as in the original papers) was a path in the tensor algebra over V with appropriate "p-...
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### Understanding of rough path

You have seen all kinds of integration theories before — Itô, Stratonovich, and I'm sure plenty others. Rough paths takes a step back and asks what we want from an integration theory. And so long as ...
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• 4,519
1 vote

### An integral by rough path.

This is an old question but it's quite interesting. Here is an attempt with some extra assumptions because $f$ and $b$ are not concrete. The reasonable approach is to try to find a Gubinelli ...
• 4,519
1 vote
Accepted

### Reference: Ito lemma for rough paths

In addition to what Nate Eldredge mentioned, here is a recent paper that you might like to consider. Keller, Christian; Zhang, Jianfeng Pathwise Itô calculus for rough paths and rough PDEs with path ...
• 42.3k

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