Stochastic invariance of closed sets with non-Lipschitz coefficients

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Jaber, Eduardo Abi^1,2  Bouchard, Bruno¹  Illand, Camille² 

[1] Univ Paris 09, PSL Univ, CEREMADE, CNRS, F-75016 Paris, France

[2] Multi Asset Client Solut, Quantitat Res, 6 Pl Pyramide, F-92908 Paris, France

关键词: Stochastic differential equation;    Stochastic invariance;    Affine diffusions;    polynomial diffusions;   

DOI  :  10.1016/j.spa.2018.06.003

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free