抛物型SPDE中假设检验的中偏差原理
Moderate Deviations of Hypothesis Testing in Stochastic Partial Differential Equations

作者: 崔汝伟 :南京航空航天大学,江苏 南京 ;

关键词: 可加分数布朗运动随机微分方程假设检验中偏差Fractional Brownian Motion Stochastic Partial Differential Equation Hypothesis Testing Moderate Deviation

摘要:
本论文的目的是研究由可加分布朗运动驱动的随机偏微分方程中漂移系数的假设检验问题,其中Hurst系数为H∈[ 21,1)。并且我们利用对数似然比的中偏差原理,在维数N固定,时间T趋于无穷的情况下,给出了未知参数的拒绝域和两类错误的衰减速度。最后我们将结果应用在几个例子当中。

Abstract: In this paper, we focus our attention on the hypothesis testing problem for the drift coefficient in the diagonalizable stochastic evolution equation driven by additive fractional Brownian motion with Hurst parameter H∈[ 21,1);. And when the dimension N is fixed and observation time T tends to infinity, with the help of moderate deviations for the log-likelihood ratio process, we give the negative regions and obtain the decay rates of the error probabilities. Moreover, we also apply our results to some examples.

文章引用: 崔汝伟 (2015) 抛物型SPDE中假设检验的中偏差原理。 理论数学, 5, 28-33. doi: 10.12677/PM.2015.52005

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