论文标题
随机效应的最大似然估计由分数布朗运动驱动
Maximum Likelihood Estimation of Stochastic Differential Equations with Random Effects Driven by Fractional Brownian Motion
论文作者
论文摘要
随机微分方程和随机动力学是描述现实世界中随机现象的好模型。在本文中，我们研究了具有实际条目的n独立的随机过程XI（t），这些过程由随机术语的随机微分方程确定，这些方程取决于某些随机效应。我们通过核转换获得了由布朗运动驱动的随机微分方程的Girsanov型公式。在随机效应的某些假设下，我们通过最大似然估计来估算参数估计器，并为离散观测值提供一些数值模拟。结果表明，对于不同的H，随着数据量的增加，参数估计器更接近真实值。
Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by the stochastic differential equations with drift term relying on some random effects. We obtain the Girsanov-type formula of the stochastic differential equation driven by Fractional Brownian Motion through kernel transformation. Under some assumptions of the random effect, we estimate the parameter estimators by the maximum likelihood estimation and give some numerical simulations for the discrete observations. Results show that for the different H, the parameter estimator is closer to the true value as the amount of data increases.
