标题： 高斯空间上的随机分析在漂移估计中的应用 显示英文标题

标题： Stochastic analysis on Gaussian space applied to drift estimation

摘要： 本文我们考虑使用Paley-Wiener和Karhunen-Loève展开对高斯过程的漂移进行非参数函数估计。我们构建了这类过程漂移的有效估计量，并通过贝叶斯估计量证明了它们的最小最大性。我们还利用Malliavin分部积分公式和高斯空间上的随机分析，构建了此类漂移的Stein类型的超有效估计量，在此过程中，过程路径的超调和泛函起着特殊的作用。我们的结果通过数值模拟进行了说明，并扩展了Berger和Wolper对高斯过程的James-Stein类型估计量的构造。 显示英文摘要

摘要： In this paper we consider the nonparametric functional estimation of the drift of Gaussian processes using Paley-Wiener and Karhunen-Lo\`eve expansions. We construct efficient estimators for the drift of such processes, and prove their minimaxity using Bayes estimators. We also construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts formula and stochastic analysis on Gaussian space, in which superharmonic functionals of the process paths play a particular role. Our results are illustrated by numerical simulations and extend the construction of James-Stein type estimators for Gaussian processes by Berger and Wolper.