Electronic Communications in Probability

Exit boundaries of multidimensional SDEs

Russell Lyons

Full-text: Open access

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.

Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 24, 2 pp.

Dates
Received: 8 February 2019
Accepted: 12 April 2019
First available in Project Euclid: 20 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1558339220

Digital Object Identifier
doi:10.1214/19-ECP231

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
inaccessible Lipschitz singular

Rights
Creative Commons Attribution 4.0 International License.

Citation

Lyons, Russell. Exit boundaries of multidimensional SDEs. Electron. Commun. Probab. 24 (2019), paper no. 24, 2 pp. doi:10.1214/19-ECP231. https://projecteuclid.org/euclid.ecp/1558339220


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References

  • [1] Alexander S. Cherny and Hans-Jürgen Engelbert, Singular stochastic differential equations, Lecture Notes in Mathematics, 1858. Springer-Verlag, Berlin, 2005.