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Stochastic invariance of closed sets with non-Lipschitz coefficients

Eduardo Abi Jaber (), Bruno Bouchard, Camille Illand () and Eduardo Jaber
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Eduardo Abi Jaber: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique
Bruno Bouchard: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique
Camille Illand: AXA Investment Managers, Multi Asset Client Solutions, Quantitative Research - AXA

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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.

Keywords: polynomial diffusions; affine diffusions; polynomial preserving diffusions; stochastic invariance; Stochastic differential equation (search for similar items in EconPapers)
Date: 2018
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01349639v3
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Published in Stochastic Processes and their Applications, Elsevier, In press, 〈10.1016/j.spa.2018.06.003〉

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