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Stochastic invariance of closed sets with non-Lipschitz coefficients

Author

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  • Eduardo Abi Jaber

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Bruno Bouchard

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Camille Illand

    (AXA Investment Managers, Multi Asset Client Solutions, Quantitative Research - AXA)

  • Eduardo Abi Jaber

Abstract

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.

Suggested Citation

  • Eduardo Abi Jaber & Bruno Bouchard & Camille Illand & Eduardo Abi Jaber, 2018. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Post-Print hal-01349639, HAL.
    • Handle: RePEc:hal:journl:hal-01349639
    DOI: 10.1016/j.spa.2018.06.003
    Note: View the original document on HAL open archive server: https://hal.science/hal-01349639v3
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