COMPARISON OF STOCHASTIC AND DETERMINISTIC MODELS OF A LINEAR CHEMICAL-REACTION WITH DIFFUSION

• 成果类型: Article
• 署名作者: BLOUNT, D
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990219
• 发表日期: 1991
• 页码: 1440-1462
• 关键词: limit

摘要

Particles placed in N cells on the unit interval give birth or die according to linear rates. Adjacent cells are coupled by diffusion with a rate proportional to N2. Cell numbers are divided by a density parameter to represent concentrations, and the resulting space-time Markov process is compared to a corresponding deterministic model, the solution to a partial differential equation. The models are viewed as Hilbert space valued processes and compared by means of a law of large numbers and central limit theorem. New and nearly optimal results are obtained by exploiting the Ornstein-Uhlenbeck type structure of the stochastic model.