Iterated integral of a path
= Iterated integral of a path
{title2=$\int_{s<u_1<\cdots<u_k<t}dx_{u_1}\otimes\cdots\otimes dx_{u_k}$}
= Iterated integrals of a path
{synonym}
For a continuous path of <bounded variation>, integrate successively over the ordered simplex using <Riemann-Stieltjes integrals>. These integrals form the levels of its <path signature>. Appending the final integration variable gives the differential recursion $dS^{(k)}_t=S^{(k-1)}_t\otimes dx_t$.