Dynamical models for the two-parameter
Poisson-Dirichlet distribution
and the Pitman-Yor process
报告专家：孙玮（加拿大康戈迪亚大学）
报告时间：7月5日（星期日）上午10:30-11:30
报告地点：数学学院西202
报告摘要：
The Pitman-Yor process is a discrete labelled random measure that has been used as a prior in Bayesian nonparametrics for the study of groups of clustered data exhibiting power law behaviour. The masses of the process in descending order follow the unlabelled two-parameter Poisson-Dirichlet distribution. In this talk, we introduce and study a family of diffusion processes associated with the Pitman-Yor process and the two-parameter Poisson-Dirichlet distribution. The diffusion coefficients indexed by a non-negative parameter $\gamma$ are smaller than the corresponding one-parameter models in terms of quadratic forms or bilinear forms when $\gamma $ is positive. The well known Petrov's diffusion corresponds to $\gamma =0$ among the unlabelled diffusions. If $\gamma$ is the same as the stable parameter $\alpha$ in the Pitman-Yor process, we obtain both labelled and unlabelled reversible diffusion processes with the Pitman-Yor process and the two-parameter Poisson-Dirichlet distribution as the corresponding reversible measures. In comparison with existing models in the literature, our models possess two fundamental new features. Firstly, our labelled model is characterized by an explicit generator, which is the first among all models studied so far. Secondly, by slowing down the diffusion in our model, the essential role of the diversity index (a multiple of local time) for the positive stable parameter is revealed in the evolution of the population. This talk is based on joint work with Shui Feng.
专家简介：
孙玮，加拿大康戈迪亚大学数学与统计系教授。1992年、1995年在四川大学分别获得学士学位和硕士学位，1998年在中国科学院数学与系统科学研究院应用数学研究所获得博士学位，导师为马志明院士。2004年入职加拿大康戈迪亚大学，2015年6月起任正教授。主要研究兴趣是随机分析、狄氏型、马氏过程，与合作者一起解决和部分解决了一些开问题，在 Ann. Appl. Probab.，Probab. Theory Related Fields, J. Funct. Anal.，J. Differential Equations，Sci. China Math.， Electron. J. Probab.等杂志发表论文70多篇。
邀请人：胡泽春
