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
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01349639
Journal nameStochastic Processes and their Applications
MetadataShow full item record
Abstract (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.
Subjects / Keywordsaffine diffusions; polynomial preserving diffusions; stochastic invariance; Stochastic differential equation
Showing items related by title and author.