Exit boundaries of multidimensional SDEs

Russell Lyons

doi:10.1214/19-ECP231

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Home > Journals > Electron. Commun. Probab. > Volume 24 > Article

2019 Exit boundaries of multidimensional SDEs

Russell Lyons

Electron. Commun. Probab. 24: 1-2 (2019). DOI: 10.1214/19-ECP231

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Abstract

We show that solutions to multidimensional SDEs with Lipschitz coefficients and driven by Brownian motion never reach the set where all coefficients vanish unless the initial position belongs to that set.