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

@article{Boedihardjo2019TheES,
  title={The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence},
  author={H. Boedihardjo and J. Diehl and M. Mezzarobba and H. Ni},
  journal={arXiv: Probability},
  year={2019}
}
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. 
The expected signature of stopped Brownian motions on 2D domains has finite radius of convergence everywhere
A fundamental question in rough path theory asks if the expected signature of geometric rough paths completely determines the law of signature. One sufficient condition for the affirmative answer isExpand

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