Stochastic invariance of closed sets with non-Lipschitz coefficients

Eduardo Abi Jaber; Bruno Bouchard; Camille Illand

doi:10.1016/j.spa.2018.06.003

Stochastic invariance of closed sets with non-Lipschitz coefficients

Eduardo Abi Jaber
, Bruno Bouchard
, Camille Illand

Research output: Contribution to journal › Article › peer-review

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 applied to construct affine and polynomial diffusions on any arbitrary closed set.

Original language	English
Pages (from-to)	1726-1748
Number of pages	23
Journal	Stochastic Processes and their Applications
Volume	129
Issue number	5
DOIs	https://doi.org/10.1016/j.spa.2018.06.003
Publication status	Published - 1 May 2019
Externally published	Yes

Keywords

Affine diffusions
Stochastic differential equation
Stochastic invariance
polynomial diffusions

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10.1016/j.spa.2018.06.003

Cite this

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title = "Stochastic invariance of closed sets with non-Lipschitz coefficients",

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 applied to construct affine and polynomial diffusions on any arbitrary closed set.",

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AU - Bouchard, Bruno

AU - Illand, Camille

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N2 - 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 applied to construct affine and polynomial diffusions on any arbitrary closed set.

AB - 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 applied to construct affine and polynomial diffusions on any arbitrary closed set.

KW - Affine diffusions

KW - Stochastic differential equation

KW - Stochastic invariance

KW - polynomial diffusions

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JF - Stochastic Processes and their Applications

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ER -

Stochastic invariance of closed sets with non-Lipschitz coefficients

Abstract

Keywords

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