The signature of a path is a sequence of tensors that encodes the geometry of the path. It is defined as the collection of iterated integrals:
\[ S(X)_{0,T} = \left(1, \int_0^T dX_t, \int_{0 < s < t < T} dX_s \otimes dX_t, \dots \right) \]
Below you can explore level 1 (net displacement) and level 2 (including the signed Lévy area) of the signature for piecewise linear paths.
implemented by Qwen 3.5