Stochastic invariance of closed sets with non-Lipschitz coefficients

被引：7

作者：

Jaber, Eduardo Abi ^{[1
,2
]}

Bouchard, Bruno ^{[1
]}

Illand, Camille ^{[2
]}

机构：

[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

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2019年 / 129卷 / 05期

关键词：

Stochastic differential equation; Stochastic invariance; Affine diffusions; polynomial diffusions; AFFINE PROCESSES; DIFFUSIONS; VIABILITY;

D O I：

10.1016/j.spa.2018.06.003

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1726 / 1748

页数：23

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