由可加分数布朗运动驱动的抛物型随机偏微分方程中极大似然估计量的中偏差原理

Moderate Deviation for Maximum Likelihood Estimator in the Parabolic Stochastic Partial Differential Equations Driven by Additive Fractional Brownian Motion

利用鞅的极限定理,本文讨论了由可加分数布朗运动驱动的抛物型随机偏微分方程中未知参数极大似然估计量的中偏差原理,给出了速率函数的精确表达式,并将主要结果应用于若干例子.

In this article, using the limit theory of martingales, we study the moderate deviation for maximum likelihood estimator of unknown parameter in the stochastic partial differential equation driven by additive fractional Brownian motion with Hurst parameter H ∈ [1/2, 1）, and the rate function can be calculated. Moreover, we apply our main result to several examples.