A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients

• 成果类型: Article
• 署名作者: Lejay, A; Martinez, M
• 署名单位: Universite de Lorraine; Universite Cote d'Azur
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000656
• 发表日期: 2006
• 页码: 107-139
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; skew-brownian-motion; euler scheme; Operators; INTEGRALS; times

摘要

The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the diffusion processes, but uses instead an exact description of the behavior of their trajectories when they reach the points of discontinuity. This description is supplied with the local comparison of the trajectories of the diffusion processes with those of a skew Brownian motion.