= Signature of a bounded variation path
{title2=$S_N(x)_{s,t}=\left(1,\int_s^t dx,\ldots,\int_{s<u_1<\cdots<u_N<t}dx_{u_1}\otimes\cdots\otimes dx_{u_N}\right)$}
= Path signature
{synonym}
= Signatures of bounded variation paths
{synonym}
The <path signature> collects the ordered iterated <Riemann-Stieltjes integrals> of a continuous path of <bounded variation>. Its truncation belongs to the <free step-N nilpotent Lie group>. It multiplies under concatenation by the <Chen identity>, is independent of orientation-preserving reparametrisation of the whole path, and records more than its endpoint displacement.
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