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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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    Cited by:

    1. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Promel, 2021. "Model-free Portfolio Theory: A Rough Path Approach," Papers 2109.01843, arXiv.org, revised Oct 2022.
    2. Aur'elien Alfonsi, 2023. "Nonnegativity preserving convolution kernels. Application to Stochastic Volterra Equations in closed convex domains and their approximation," Papers 2302.07758, arXiv.org, revised Oct 2024.

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