﻿ 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

Pure Mathematics
Vol.05 No.02(2015), Article ID:14897,5 pages
10.12677/PM.2015.52005

Moderate Deviations of Hypothesis Testing in Stochastic Partial Differential Equations

Ruwei Cui

Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu

Email: cuiruwei@126.com

Received: Feb. 12th, 2015; accepted: Feb. 25th, 2015; published: Mar. 2nd, 2015

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. 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.

Keywords:Fractional Brownian Motion, Stochastic Partial Differential Equation, Hypothesis Testing, Moderate Deviation

Email: cuiruwei@126.com

1. 介绍

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Demo [2] 给出了鞅的中偏差原理。若方程为可对角化的抛物型方程，Cialenco，Lototsky和Pospisil [1] 给出了参数估计量的大数定律和中心极限定理。同时Hu和Nualart [3] 通过研究对数似然率的大偏差原理，分别在时间和维数趋于无穷的时候构造了相应的假设检验拒绝域。

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2. 定理的证明

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，根据Girsanov公式我们可以看出

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3. 应用

1) 考虑如下方程：

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2) 考虑如下方程：

Moderate Deviations of Hypothesis Testing in Stochastic Partial Differential Equations. 理论数学,02,28-33. doi: 10.12677/PM.2015.52005

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