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3
votes
1answer
182 views

Understand rough path iterated integral and how to compute it numerically?

The "signature" of rough path theory is defined by iterated integral as $s(k)=\int_{0 \le u_1 \le \cdots \le u_k \le t} \mathrm{d}X_{u_1} \otimes \cdots \otimes \mathrm{d}X_{u_k}$ in witch $X(t)$ is ...
2
votes
0answers
128 views

Chen's iterated integrals and free loop space

I recently found out about Chen's iterated integrals for paths in a differentiable manifold, and I was wondering if an analogous construction exists for free loops, i.e. a set of variables one ...
4
votes
0answers
203 views

Restriction of iterated integrals

For a smooth manifold $X$, let $B_s(X)$ denote the space of iterated integrals of length at most $s$. Here we consider iterated integrals as functions on the path space $PX$. Fix a base point $x_0$ ...
14
votes
3answers
2k views

Understanding iterated integrals

I have encountered iterated integrals on papers dealing with multizeta values, polylogarithms etc.. Since then I am trying to figure out the motivations and purpose of the theory. It seems the ...