Stochastic invariance of closed sets with non-Lipschitz coefficients

Abi Jaber, Eduardo; Bouchard, Bruno; Illand, Camille

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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Type

Article accepté pour publication ou publié

External document link

https://hal.archives-ouvertes.fr/hal-01349639

Date

2019

Journal name

Stochastic Processes and their Applications

Volume

129

Number

Publisher

Elsevier

Pages

1726-1748

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 / Keywords

affine diffusions; polynomial preserving diffusions; stochastic invariance; Stochastic differential equation