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Academic Report

DATE:2019-07-01 23:15   NUM:

Report Title:Longtime behavior of Levy-driven Ornstein-Uhlenbeck process with regime-switching

Report Expert:Shao Jinghai Professor of TianjinUniversity

Report Location:9-122

Report Time:2019-7-2 4: 30-5: 30 PM

Abstract:Theprocesses with regime switching can be used to characterize a stochasticdynamical system in a random environment. We investigate the long time behaviorof the Ornstein Uhlenbeck process driven by Levy noise with regime switching.We provide explicit c riteria on the transience and recurrence of this process.Contrasted with the Ornstein Uhlenbeck process driven simply by Brownianmotion, whose stationary distribution must be light tailed, both the jumpscaused by the Levy noise and regime switching desc ribed by Markov chain canderive the heavy tailed property of the stationary distribution. In this work,the different role played by Levy measure and regime switching process isclearly characterized.

Briefintroduction of the speaker: Shao Jinghai, obtainedPh.D. degrees from Beijing Normal University and Dijon University in France in2006. During the same year, he taught at Beijing Normal University. He washired as an associate professor in 2010. In 2007, he went to the University ofBern, Germany to follow Professor K. Sturm as a postdoctoral researcher for twoyears. In 2017, he was hired as a professor by Tianjin University. ProfessorShao is mainly engaged in research work on probability theory ergodic theory,stochastic analysis, stochastic differential equations. Many papers have beenpublished in famous mathematical journals, including J. Functional Analysis,Probability Theory and Related Fields, SIAM J. Control Optim, SIAM J. Math.Anal., Stochastic Processes and their Applications. In 2007, Professor ShaoJinghai won the “Zhong Jiaqing Mathematics Award” of the Chinese Mathematical Association.In 2008, he won the National 100 Excellent Doctoral DissertationAwards


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