【题目】Hawkes自激发过程和无穷服务台排队系统
【时间】2017年12月13日 (周三)13:30-15:00
Xuefeng Gao is an Assistant Professor at the Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong. He received his B.S. in Mathematics from Peking University, China in 2008, and his Ph.D. in Operations Research from Georgia Institute of Technology, USA in 2013. His research interests include stochastic models with applications in finance and queueing. His work has been selected as Finalist in the 2011 INFORMS Junior Faculty Interest Group (JFIG) paper competition.
【摘要】A univariate Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process is given by the sum of a baseline intensity and another term that depends on the entire past history of the point process. Hawkes process has wide applications in finance, social networks, online advertisements, neuroscience, criminology, seismology, and many other fields. In this paper, we prove a functional central limit theorem for stationary Hawkes processes in the asymptotic regime where the baseline intensity is large. The limit is a non-Markovian Gaussian process with dependent increments. We use the resulting approximation to study an infinite-server queue with high-volume Hawkes traffic. We show that the queue length process can be approximated by a Gaussian process, for which we compute explicitly the covariance function and the steady-state distribution. We also extend our results to multivariate stationary Hawkes processes and establish limit theorems for infinite-server queues with multivariate Hawkes traffic. This is a joint work with Lingjiong Zhu from Florida State University.
Xuefeng Gao, Assistant Professor, The Chinese University of Hong Kong：Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues
【Speaker】Xuefeng Gao, Assistant Professor, The Chinese University of Hong Kong
【Title】Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues
【Time】Dec 13，Wednesday, 13:30-15:00
【Venue】Room 501, Weilun Building, Tsinghua SEM
【Organizer】Department of Management Science and Engineering
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