报告题目：An introduction to self-similar Markov processes.

报 告 人：Loïc Chaumont（University of Angers, France）

报告时间：2022年6月20日20:00-21:00

报告地点：腾讯会议ID:876 307 453

报告摘要：An Rd-valued stochastic process is said to be self-similar if its image by
any linear time change has the same law as its image by a linear dilation of space.
They often appear in practice as scaling limits of time changed stochastic processes.
The self-similarity of Brownian motion was highlighted in the 1940s by Paul Lévy
who also, later on, considered the example of stable processes. This notion was then
defined in a very general context by Lamperti in the early 1960s. Self-similar processes enjoy particular distribution or trajectory properties depending on whether
they are Markovian, have independent increments or have stationary increments. In
each case, Lévy processes are involved in their construction through path representations. This lecture aim to introduce the main classes of self-similar processes of which a common element is a Brownian motion. We will pay particular attention to the case of Markovian processes that we will approach through the famous Lamperti representation. The example of stable Lévy processes and some of their conditioned versions will be studied in more detail.

个人简介：

    Lo¨ıc CHAUMONT, Professor, University of Angers (France)

Main research interests:

• Random walks and L´ evy processes.

(Fluctuation theory, invariance principles, problems of persistence)

• Self-similar Markov processes.

(Lamperti representation, potential theory)

• Branching processes and branching trees.

(Coding of multitype trees, study of extinction and conservativeness)

Main administrative responsabilities

• Co-director of the SFR MathSTIC (federation of scientific laboratories) at the Uni-

versity of Angers since January 2017.

• Member of the scientific council of the Labex Henri Lebesgue (federation of math-

ematics departments in the North West of France) from January 2013 to December

2018.

• Director of LAREMA, UMR CNRS 6093 (mathematics department of the University

of Angers) from January 2012 to December 2016.

• Member of the scientific council of the University of Angers from 2012 to 2016.

• Deputy Director of the doctoral school STIM (Sciences et Technologies de l’Information,

Math´ ematiques) in the North West of France from 2008 to 2012

Publications and scientific productions:

51 articles published in international journals with reviewing committee, 1 book and 3 collective works.