# 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

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.

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