The logarithm of the expected path signature satisfies ordered-partition analogues of classical cumulant formulas, giving an independence test and efficient estimators for path-valued data.
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Signature Cumulants, Ordered Partitions, and Independence of Stochastic Processes
The logarithm of the expected path signature satisfies ordered-partition analogues of classical cumulant formulas, giving an independence test and efficient estimators for path-valued data.