Electronic Communications in Probability

Stochastic invariance of closed sets for jump-diffusions with non-Lipschitz coefficients

Eduardo Abi Jaber

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We provide necessary and sufficient first order geometric conditions for the stochastic invariance of a closed subset of $\mathbb{R} ^d$ with respect to a jump-diffusion under weak regularity assumptions on the coefficients. Our main result extends the recent characterization proved in Abi Jaber, Bouchard and Illand (2016) to jump-diffusions. We also derive an equivalent formulation in the semimartingale framework.

Article information

Electron. Commun. Probab., Volume 22 (2017), paper no. 53, 15 pp.

Received: 21 December 2016
Accepted: 15 September 2017
First available in Project Euclid: 13 October 2017

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Zentralblatt MATH identifier

Primary: 93E03: Stochastic systems, general 60H10: Stochastic ordinary differential equations [See also 34F05] 60J75: Jump processes

stochastic differential equation jumps semimartingale stochastic invariance

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Abi Jaber, Eduardo. Stochastic invariance of closed sets for jump-diffusions with non-Lipschitz coefficients. Electron. Commun. Probab. 22 (2017), paper no. 53, 15 pp. doi:10.1214/17-ECP88. https://projecteuclid.org/euclid.ecp/1507860210

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