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May 2016 On approximate continuity and the support of reflected stochastic differential equations
Jiagang Ren, Jing Wu
Ann. Probab. 44(3): 2064-2116 (May 2016). DOI: 10.1214/15-AOP1018

Abstract

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.

Citation

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Jiagang Ren. Jing Wu. "On approximate continuity and the support of reflected stochastic differential equations." Ann. Probab. 44 (3) 2064 - 2116, May 2016. https://doi.org/10.1214/15-AOP1018

Information

Received: 1 October 2014; Revised: 1 March 2015; Published: May 2016
First available in Project Euclid: 16 May 2016

zbMATH: 1347.60072
MathSciNet: MR3502601
Digital Object Identifier: 10.1214/15-AOP1018

Subjects:
Primary: 60H10 , 60H99
Secondary: 60F99

Keywords: approximate continuity , limit theorem , maximum principle , Reflected stochastic differential equation , Support

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 3 • May 2016
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