The Annals of Probability

On approximate continuity and the support of reflected stochastic differential equations

Jiagang Ren and Jing Wu

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In this paper we prove an approximate continuity result for stochastic differential equations with normal reflections in domains satisfying Saisho’s conditions, which together with the Wong–Zakai approximation result completes the support theorem for such diffusions in the uniform convergence topology. Also by adapting Millet and Sanz-Solé’s idea, we characterize in Hölder norm the support of diffusions reflected in domains satisfying the Lions–Sznitman conditions by proving limit theorems of adapted interpolations. Finally we apply the support theorem to establish a boundary-interior maximum principle for subharmonic functions.

Article information

Ann. Probab., Volume 44, Number 3 (2016), 2064-2116.

Received: October 2014
Revised: March 2015
First available in Project Euclid: 16 May 2016

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H99: None of the above, but in this section
Secondary: 60F99: None of the above, but in this section

Reflected stochastic differential equation approximate continuity support limit theorem maximum principle


Ren, Jiagang; Wu, Jing. On approximate continuity and the support of reflected stochastic differential equations. Ann. Probab. 44 (2016), no. 3, 2064--2116. doi:10.1214/15-AOP1018.

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