On approximate continuity and the support of reflected stochastic differential equations

• Ren, Jiagang ^[1] ; Wu, Jing ^[1]
  1. [1] Sun Yat-sen University

     Sun Yat-sen University

     China

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 3, 2016, págs. 2064-2116
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.