Signature moments to characterize laws of stochastic processes

Ilya Chevyrev, Harald Oberhauser

Research output: Contribution to journalArticlepeer-review

Abstract

The normalized sequence of moments characterizes the law of any finite-dimensional random variable. We prove an analogous result for path-valued random variables, that is stochastic processes, by using the normalized sequence of signature moments. We use this to define a metric for laws of stochastic processes. This metric can be efficiently estimated from finite samples, even if the stochastic processes themselves evolve in high-dimensional state spaces. As an application, we provide a non-parametric two-sample hypothesis test for laws of stochastic processes.
Original languageEnglish
Number of pages42
JournalJournal of Machine Learning Research
Publication statusAccepted/In press - 5 Jun 2022

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