Statistics and Probability Seminar

Probabilistic Symmetries and Random Locations
Friday, 22 September 2017 - 1:30 pm to 2:00 pm
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    SPEAKER: Yi Shen (University of Waterloo)             ABSTRACT: In this talk we briefly discuss different types of symmetries in probability, including stationarity, stationarity of the increments, isotropy, self-similarity, exchangeability, and their combinations. Each of these symmetries is naturally related to an operator in the path space, in the sense that the symmetry can be expressed as the invariance of the distribution of the stochastic processes with respect to the corresponding operator. In particular, we consider the random locations of the stochastic processes, such as the hitting times or the location of the path supremum over a fixed interval. On one hand, we see how the probabilistic symmetries can imply the properties of the distributions of these random locations; on the other hand, we also discuss how the distributions of the random locations can be used to characterize the probabilistic symmetries. This talk is based on joint works with Gennady Samorodnitsky, Shunlong Luo and Jie Shen.