Stochastic particle approximations for Smoluchoski's coagulation equation

• 成果类型: Article
• 署名作者: Eibeck, A; Wagner, W
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2001
• 页码: 1137-1165
• 关键词: gelation; models

摘要

This paper studies stochastic particle approximations for Smoluchowski's coagulation equation. A new stochastic algorithm with reduced variance is proposed. Its convergence behavior is investigated, when the number of simulation particles tends to infinity. Under appropriate assumptions on the coagulation kernel, the limit is the unique solution of the coagulation equation. Then detailed numerical experiments are performed, testing the applicability and efficiency of the algorithm. In particular, the gelation phenomenon (loss of mass in the coagulation equation) is studied numerically for several kernels. A striking feature of the new algorithm is a better convergence after the gelation point, providing a tool for detecting the mass of the gel.