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Stochastic invariance of closed sets with non-Lipschitz coefficients

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

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.

Suggested Citation

  • Abi Jaber, Eduardo & Bouchard, Bruno & Illand, Camille, 2019. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1726-1748.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:5:p:1726-1748
    DOI: 10.1016/j.spa.2018.06.003
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    References listed on IDEAS

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