Open Access
2017 Stochastic invariance of closed sets for jump-diffusions with non-Lipschitz coefficients
Eduardo Abi Jaber
Electron. Commun. Probab. 22: 1-15 (2017). DOI: 10.1214/17-ECP88


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.


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Eduardo Abi Jaber. "Stochastic invariance of closed sets for jump-diffusions with non-Lipschitz coefficients." Electron. Commun. Probab. 22 1 - 15, 2017.


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

zbMATH: 1373.93307
MathSciNet: MR3718703
Digital Object Identifier: 10.1214/17-ECP88

Primary: 60H10 , 60J75 , 93E03

Keywords: jumps , Semimartingale , Stochastic differential equation , stochastic invariance

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