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

利用大数定律和中心极限定理，比较了具有扩散的化学反应的随机模型和确定性模型。所提出的方法将比以往的工作更充分地利用相关压缩半群的光滑性，并反映潜在的大偏差行为。所发展的方法可用于证明具有不连续和非高斯鞅项的随机发展方程的正则性结果。随机模型将被重新表述为度量值扩散。这位研究者在概率领域工作，在随机过程领域工作。他正在研究化学反应的模型，在过去的15年里，其他研究人员一直在积极研究这些模型。他的结果不仅将大大有助于理解这些反应，而且还将有助于数学家在解决某些问题时使用的一套工具。

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.