可对角化双线性随机抛物型方程的参数估计
Parameter estimation in diagonalizable bilinear stochastic parabolic equations
摘要：
考虑了一类带乘性噪声的随机抛物型方程的参数估计问题，假定该方程可化为一个无限非耦合扩散过程系统.从经典统计学的观点来看，这个问题不仅对原来的无限维系统是奇异的，而且对大多数有限维投影也是奇异的。这种奇异性可以用来提高传统估计的收敛速率，也可以用来构造全新的闭型精确估计。
英文摘要：
A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion processes. From the point of view of classical statistics, this problem turns out to be singular not only for the original infinite-dimensional system but also for most finite-dimensional projections. This singularity can be exploited to improve the rate of convergence of traditional estimators as well as to construct completely new closed-form exact estimator.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
