On an Inversion Theorem for Stratonovich's Signatures of Multidimensional Diffusion Paths

2013/04/25 by Xi Geng, Zhongmin Qian, Geng, Xi +1
Computer Science · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Topological and Geometric Data Analysis #advanced mathematical theories #math.PR

paper · pdf · doi:10.48550/arxiv.1304.6985

openalex publication_date 2013/04/25 · arxiv created 2014/10/26 · arxiv updated 2014/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we prove that with probability one, the Stratonovich signatures of a multidimensional diffusion process (possibly degenerate) over [0,1], which is the collection of all iterated Stratonovich's integrals of the diffusion process over [0,1], determine the diffusion sample paths.

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