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

DOI10.1112/blms.12420zbMath1486.60124arXiv1905.13034OpenAlexW2946892435MaRDI QIDQ4996913

Horatio Boedihardjo, Joscha Diehl, Marc Mezzarobba, Hao Ni

Publication date: 2 July 2021

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.13034

zbMATH Keywords

Brownian motionrough pathsexpected signature

Mathematics Subject Classification ID

Brownian motion (60J65) PDEs with randomness, stochastic partial differential equations (35R60) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Signatures and data streams (60L10)

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Expected signature of stopped Brownian motion on \(d\)-dimensional \(C^{2, \alpha }\)-domains has finite radius of convergence everywhere: \(2 \leq d \leq 8\) ⋮ Signature-Based Models: Theory and Calibration ⋮ Topologies on unparameterised path space ⋮ Sig‐Wasserstein GANs for conditional time series generation

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