报告题目一: Large deviation principles for first-order scalar conservation laws with stochastic forcing
报 告 人: 董昭 教授（中国科学院数学与系统科学研究院）
报告摘要：In this paper, we established the Freidlin-Wentzell type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for Abstract 15 these first-order conservation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach. This is joint work with Wu Jiang Lun, Zhang Rang Rang, Zhang Tu sheng.
报告题目二: Distribution with the semi-regular-variation tail and its applications
报 告 人: 王岳宝 教授（苏州大学数学科学学院）
报告摘要：In this talk, we divide the exponential distribution class into some subclasses according to a certain criterion. One of them is closely related to the regular variation-tailed distribution class and is called the semi-regular-variation-tailed distribution class. We give the precise tail asymptotic expression for the convolutions of these distributions, and prove that the class is closed under convolution. In addition, the corresponding random variables are not necessarily identically distributed. Finally, we apply these results to a discrete time risk model with stochastic returns, and obtain the precise asymptotic estimation of the finite time ruin probability.
报告题目三: Asymptotic behavior for ruin probabilities in some generalized bidimensional risk models
报 告 人: 程东亚 教授（苏州大学数学科学学院）
报告摘要：In this talk, we consider asymptotic behavior for ruin probabilities in some generalized bidimensional continuous-time risk models with heavy-tailed claims. In these models, dependent relation exists either between the components of each pair of the claim sizes or among the claim sizes from each lines of business. As for the claim-number processes, they are allowed to be arbitrarily dependent. We introduced four types of finite-time ruin probabilities and for each type of ruin, an asymptotic formula for the finite-time ruin probability is established. Some of these formulae possess a certain uniformity feature in the time horizon. The obtained results confirm that the Brownian perturbations have no influence on the asymptotics of the ruin probabilities under consideration.