Stochastic invariance of closed sets with non-Lipschitz coefficients

Eduardo Abi Jaber, Bruno Bouchard and Camille Illand

Stochastic Processes and their Applications, 2019, vol. 129, issue 5, 1726-1748

Abstract: This paper provides a new characterization of the stochastic invariance of a closed subset of Rd 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 applied to construct affine and polynomial diffusions on any arbitrary closed set.

Keywords: Stochastic differential equation; Stochastic invariance; Affine diffusions; polynomial diffusions (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2018.06.003

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