报告人：谷伟（中南财经政法大学）

报告题目: Estimation for a type of diffusion process observed with measurement error

报告摘要：An improved filtering method is provided to estimate the parameter for a type of nonlinear multivariate stochastic differential equations (SDEs) with multiplicative noise, when discrete observations contaminated with measurement error are given. First, a transformation is used to transform the diffusion terms of the SDEs into unit diffusion such that the improved filtering method can be used. After the transformation, the drift terms of the SDEs are local linearized by means of Itô formula rather than Taylor expansion, and the predictions of the innovation estimators are approximated by a more rigorous theoretical form which guarantees that the improved method works well even when the Jacobian matrix of the drift terms is singular or ill-conditioned. The parameter is estimated from discrete observations by maximum likelihood technique. The improved method is compared to an existing software tool CTSM by estimating Van der Pol’s random oscillation with unobserved state variables, the provided method proves to be robust particularly when observation noise is relatively large. Applying the improved method to modified stochastic Lotka–Volterra equations with multiplicative noise, where the performance of the linear approximation by Itô formula and Taylor expansion is compared, in conclusion the provided method has better performance especially under long observation time interval.

报告人简介：谷伟，男，博士，中南财经政法大学副教授，硕导，文澜青年学者。2008年毕业于申博sunbet官网，2015.3-2016.3，佛罗里达大西洋大学，数学学院，访问学者，2009.2-2010.8, 美国罗切斯特大学，生物统计及计算生物系，访问学者。主要研究兴趣：金融随机模型参数估计及应用，统计计算，金融市场风险度量，大数据探索性分析及数据挖掘技术。发表过10多篇SCE期刊论文论文，出版学术专著一部,主持国家自然科学基金1项，主持省部级以上科究项目2项，主持校级科研项目5项，参与国家自然科学基金3项。

报告时间：2019年5月7日（星期二）上午9:30
报告地点：科技楼南楼702室