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arXiv · 1905.13034

The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence

Horatio Boedihardjo·Joscha Diehl·Marc Mezzarobba·Hao Ni
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Abstract

The expected signature is an analogue of the Laplace transform for rough paths. Chevyrev and Lyons showed that, under certain moment conditions, the expected signature determines the laws of signatures. Lyons and Ni posed the question of whether the expected signature of Brownian motion up to the exit time of a domain satisfies Chevyrev and Lyons' moment condition. We provide the first example where the answer is negative.

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Horatio Boedihardjo, Joscha Diehl, Marc Mezzarobba, Hao Ni. 2019-05-30. The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence. https://doi.org/10.1112/blms.12420

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