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学术报告
学术报告
威尼斯官方网站登录百年校庆威尼斯官方网站系列学术报告之六十八 丹麦哥本哈根大学Xu Chuang 博士学术报告通知
发布人:蔡易??威尼斯官方网站:2019-12-26?? 浏览次数:353

    应威尼斯官方网站王春程老师的邀请,丹麦哥本哈根大学(University of Copenhagen)Xu

Chuang博士将于近日来访我校并做报告,欢迎感兴趣的师生参加。

    时间:201912291600-1700

    地点:格物楼503

       Title: Dynamics of continuous time Markov chains with applications to stochastic reaction networks

      Abstract:In this talk I will present our recent work on the properties of continuous time Markov chains (CTMCs) on non-negative integer lattices, with particular interest in one-dimensional CTMCs with polynomial transitions rates. Such stochastic processes are abundant in applications, in particular within biology. We study the classification of states for general CTMCs on the non-negative integer lattices, by characterizing the set of absorbing states (similarly, trapping, escaping, positive irreducible components and quasi-irreducible components). For CTMCs on non-negative integers with polynomial transition rates, we provide threshold criteria in terms of easily computable parameters for various dynamical properties such as explosivity, recurrence, transience, positive/null recurrence, implosivity, and existence and non-existence of passage times. In particular, simple sufficient conditions for exponential ergodicity of stationary distributions and quasi-stationary distributions are obtained. Moreover, an identity for stationary measures is established and tail asymptotics for stationary distributions is given. A similar identity as well as asymptotics is derived for quasi-stationary distributions. Finally, we apply our results to stochastic reaction networks. This is a joint work with Mads Christian Hansen and Carsten Wiuf. 


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