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Stochastic invariance of closed sets with non-Lipschitz coefficients

Abi Jaber, Eduardo; Bouchard, Bruno; Illand, Camille (2019), Stochastic invariance of closed sets with non-Lipschitz coefficients, Stochastic Processes and their Applications, 129, 5, p. 1726-1748. 10.1016/j.spa.2018.06.003

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https://hal.archives-ouvertes.fr/hal-01349639
Date
2019
Nom de la revue
Stochastic Processes and their Applications
Volume
129
Numéro
5
Éditeur
Elsevier
Pages
1726-1748
Identifiant publication
Métadonnées
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Auteur(s)
Abi Jaber, Eduardo

Bouchard, Bruno

Illand, Camille
Résumé (EN)
This paper provides a new characterization of the stochastic invariance of a closed subset of R^d with respect to a diffusion. We extend the well-known inward pointing Stratonovich drift condition to the case where the diffusion matrix can fail to be differentiable: we only assume that the covariance matrix is. In particular, our result can be directly applied to construct affine diffusions and polynomial preserving diffusions on any arbitrary closed set.
Mots-clés
affine diffusions; polynomial preserving diffusions; stochastic invariance; Stochastic differential equation