Mathematical Sciences: Parameter Estimation for Stochastic Partial Differential Equations

摘要本项目涉及随机偏微分方程统计方法的发展研究。有两个主要问题需要调查。第一个问题是关于出现在双曲型随机偏微分方程中的参数估计，而第二个问题是关于具有非恒定参数的方程的离散版本的估计量的构造。该项目的结果可以应用于经济学、海洋学、物理化学和工程学等领域，在这些领域中，随机微分方程通常表示具有随机扰动的复杂物理系统。要估计的参数在技术装置的设计中起着至关重要的作用，但往往没有足够的准确性。为了更好地利用资源，从经济和生态的角度优化这些设备的性能是可取的。

9509000 Huebner Abstract This project involves research in the development of statistical methods for stochastic partial differential equations. Two main problems are to be investigated. The first concerns the estimation of parameters occurring in hyperbolic stochastic partial differential equations, while the second concerns the construction of estimators for discretized versions of the equations with nonconstant parameters. The results of this project can be applied to areas such as economics, oceanography, physical chemistry, and engineering, where stochastic differential equations often represent complex physical systems with random perturbations. The parameters to be estimated play a critical role in the design of technological devices and are often not known with adequate accuracy. It is desirable to optimize the performance of such devices--both from the standpoint of economy and ecology--for a better utilization of resources.