Viability property for multi-dimensional stochastic differential equation and its applications to comparison theorem

Xuejun Shi

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 2, 378-397

Abstract: In this paper, we focus on the problem of viability property for the multi-dimensional stochastic differential equations, where the coefficients of the stochastic differential equations may be random and discontinuous in the time variable. First, we establish a necessary and sufficient condition for viability property with respect to a given non-empty closed convex set. And furthermore, with the help of this result, we also study the multi-dimensional comparison theorems about stochastic differential equations.

Date: 2023
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DOI: 10.1080/03610926.2021.1914098

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