A SYSTEM OF COALESCING HEAVY DIFFUSION PARTICLES ON THE REAL LINE

• 成果类型: Article
• 署名作者: Konarovskyi, Vitalii
• 署名单位: Max Planck Society; Ministry of Education & Science of Ukraine; Yuri Fedkovych Chernivtsi National University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1137
• 发表日期: 2017
• 页码: 3293-3335
• 关键词: valued branching diffusions; arratia flow; coagulation; limit; time

摘要

We construct a modified Arratia flow with mass and energy conservation. We suppose that particles have a mass obeying the conservation law, and their diffusion is inversely proportional to the mass. Our main result asserts that such a system exists under the assumption of the uniform mass distribution on an interval at the starting moment. We introduce a stochastic integral with respect to such a flow and obtain the total local time as the density of the occupation measure for all particles.