Mathematical Sciences: Comparison of Stochastic and Deterministic Models of a Chemical reaction with Diffusion

数学科学：扩散化学反应的随机模型和确定性模型的比较

• 批准号: 8811738
• 负责人: Douglas Blount
• 金额: $ 2.84万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-11-15 至 1991-05-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8811738&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Comparison; Stochastic; Deterministic

By means of a law of large numbers and central limit theorem, the author wishes to compare stochastic and deterministic models of a chemical reaction with diffusion. The proposed methods will exploit the smoothing properties of the relevant contraction semigroup more fully than previous work and reflect underlying large deviation behavior. The methods developed can be used for proving regularity results for stochastic evolution equations having a discontinuous and non Gaussian martingale term. The stochastic model is to be reformulated as a measure valued diffusion. This investigator works in the field of probability, in the area of stochastic processes. He is working on models of chemical reactions which have been actively investigated by other researchers for the last 15 years. His results will not only significantly aid in the understanding of these reactions but will also contribute to the set of tools mathematicians employ in attacking certain problems.

利用大数定律和中心极限 定理，作者希望比较随机和 扩散化学反应的确定性模型。 的 所提出的方法将利用 相关的压缩半群，比以前的工作， 反映了潜在的大偏差行为。 的方法 开发的可用于证明规律性的结果， 随机发展方程具有不连续性和非连续性 高斯鞅项 随机模型是 重新表述为测度值扩散。 这位调查员在概率领域工作， 随机过程领域。 他正在研究 化学反应，已积极研究其他 研究人员在过去的15年里。 他的成果不仅 对理解这些反应有很大帮助， 也将有助于数学家在数学中使用的一套工具， 解决某些问题。