Expected signature of Brownian motion up to the first exit time from a bounded domain

DOI10.1214/14-AOP949zbMath1350.60086arXiv1101.5902MaRDI QIDQ888541

Hao Ni, Terence J. Lyons

Publication date: 30 October 2015

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.5902

zbMATH Keywords

cubaturediffusionBrownian motionfirst-exit timerough pathexpected signature

Mathematics Subject Classification ID

Brownian motion (60J65) Markov semigroups and applications to diffusion processes (47D07) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Heat equation (35K05) Groups and semigroups of linear operators (47D03) Stopping times; optimal stopping problems; gambling theory (60G40) Diffusion processes (60J60) Transition functions, generators and resolvents (60J35) Second-order parabolic equations (35K10) Heat kernel (35K08) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (7)

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 ⋮ Numerical Method for Model-free Pricing of Exotic Derivatives in Discrete Time Using Rough Path Signatures ⋮ Sig‐Wasserstein GANs for conditional time series generation ⋮ Canonical RDEs and general semimartingales as rough paths ⋮ The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence ⋮ Unified signature cumulants and generalized Magnus expansions

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• Stochastic differential equations. An introduction with applications.

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