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-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

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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: Stochastic differential equation; stochastic invariance; polynomial preserving diffusions; affine diffusions; polynomial diffusions (search for similar items in EconPapers)
Date: 2018
Note: View the original document on HAL open archive server: https://hal.science/hal-01349639v3
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Stochastic Processes and their Applications, 2018, 129 (5), pp.1726-1748. ⟨10.1016/j.spa.2018.06.003⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01349639

DOI: 10.1016/j.spa.2018.06.003

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