## Weak dependence and applications

#### 科研大讨论系列报告

### 报告题目(Title)：**Weak dependence and applications**

报告人(Speaker)：*Paul Doukhan（Paris Cergy University）*

地点(Place)：*后主楼1124*

时间(Time)：*2024年6月14日下午2:00-3:00*

邀请人(Inviter)：*高志强*

### 报告摘要

In the talk I will enlight in a very elementary way the issues of dependence conditions; indeed departing from independence is a delicate issue and we thus come carefully on simple conditions and examples of extensions. I was working on mixing type conditions (my 1994 monograph is cited more than 2300 times) and I realized that something was missing since such nice strong mixing conditions (developed at there summum in the 201 monograph by Rio) do not hold. In 1999 I thus introduced with Louhichi a more convenient weak dependence condition.

In the talk I will investigate some models in order to prove how adapted are those notions as well as a few number of applications of those techniques in order to prove that they may be useful.

In the talk I will investigate some models in order to prove how adapted are those notions as well as a few number of applications of those techniques in order to prove that they may be useful.

### 主讲人简介

Paul Doukhan is an expert of dependence conditions and their applications to statistics and time series, he is emeritus professor at Paris Cergy University, in the past he was senior member of French Universitary Institute and wrote around 200 papers cited more than 8000 times. He aim at understanding, analysing and fitting dependent random models, such as time series, random fields, random processes or point processes. His mathematical background led me to introduce new models, as well as to fit and test them. For this, he was the advisor for 20 PhD or Habilitation theses. As demonstrated by his two most cited monographs, he is involved into probabilistic dependence structures such as strong mixing or long range dependence. To relax usual mixing conditions, he introduced weak dependence with Sana Louhichi. Before this he introduced wavelets in statistics, which had important developments.

Applications of dependence to deal with are significant in various disciplines such as insurance, astronomy, and others. Ecology is one essential problem of the century, to which he dedicates in the Ecodep project.

Applications of dependence to deal with are significant in various disciplines such as insurance, astronomy, and others. Ecology is one essential problem of the century, to which he dedicates in the Ecodep project.