主講人：Ng, Hon Keung Tony (Department of Mathematical Sciences, Bentley University, Waltham, Massachusetts, USA)
題 目：Semiparametric and Nonparametric Evaluation of First-Passage Distribution of Bivariate Degradation Processes
日 期：113年3月12日（星期二）
時 間：下午13:30開始
地 點：科學館S433
摘要Abstract: In system engineering, the reliability of a system depends on the reliability of each subsystem (or component); those subsystems have their own performance characteristics, which can be dependent. The degradation of those dependent performance characteristics of the subsystems is used to assess the system’s reliability. Parametric frameworks have been developed to model bivariate and multivariate degradation processes in the literature; however, in practical situations, the underlying degradation process of a subsystem is usually unknown. In this work, we proposed different semiparametric and nonparametric methods to estimate the dependence bivariate degradation data's first passage time distribution. The saddlepoint approximation and bootstrap methods are used to estimate the marginal FPT distributions empirically, and the empirical copula is used to estimate the joint distribution of two dependence degradation processes nonparametrically. A Monte Carlo simulation study and a numerical example are used to demonstrate the effectiveness and robustness of the proposed semiparametric and nonparametric approaches.
主講人：劉念麟 教授(日本東京理科大學) 題 目：Spot covariance estimation with synchronous high-frequency finance data 日 期：113年2月20日（星期二） 時 間：下午14:10開始 地 點：科學館S433 摘要Abstract: Empirical studies have pointed out the importance of considering different temporal variations in correlations between asset prices. Currently, high-frequency profiles sampled asynchronously across different assets have mainly applied for integrated covariance estimation but less so for spot covariance estimation. Based on the seminal works of Malliavin and Mancino [1,2] in conjunction with the principle component analysis approach, in this talk, we try to propose a novel spot covariance estimation with synchronous high-frequency finance data. We will point out which kind of high-frequency data we are interested in and briefly explain why we apply the Malliavin-Mancino method to these data. References [1] P. Malliavin and M. E. Mancino. Fourier series method for measurement of multivariate volatilities. Finance Stoch., 6(1):49–61, 2002. [2] P. Malliavin and M. E. Mancino. A Fourier transform method for nonparametric estimation of multivariate volatility. Ann. Statist., 37(4):1983–2010, 2009.
主講人：邱鴻麟 教授(國立清華大學數學系)
題 目：Introduction to Pseudo-Hermitian geometry
日 期：113年1月2日（星期二）
時 間：下午14:10開始
地 點：科學館S433
摘要Abstract: Pseudo-Hermitian geometry came from the Several Complex Variables. It is actually a branch of Kleinian geometry. The corresponding flat space is the Heisenberg group. In this talk, I am going to make a basic introduction to this geometry
學術演講--112/12/19 崔茂培 教授(國立臺灣大學數學系)
題 目：Singular values and the deformation of maps by heat flow
日 期：112年12月19日（星期二）
時 間：下午14:10開始
地 點：科學館S433
摘要Abstract: Understanding the homotopy of maps has been a central question in topology. In this talk, we will explore how the gradient flow of certain energy functionals defined on the singular values of maps can be employed to study the deformation of maps. Two notable examples are harmonic map heat flow and graphical mean curvature flow. We will delve into recent advancements in these areas.