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

Abi Jaber, Eduardo (2017), Stochastic invariance of closed sets for jump-diffusions with non-Lipschitz coefficients, Electronic Communications in Probability, 22, paper n°53. 10.1214/17-ECP88

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
Electronic Communications in Probability
Volume
22
Number
paper n°53
Publisher
University of Washington
Publication identifier
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Author(s)
Abi Jaber, Eduardo
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We provide necessary and sufficient first order geometric conditions for the stochastic invariance of a closed subset of 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.
Subjects / Keywords
semimartingale; jumps; Stochastic differential equation; stochastic invariance