On the additive functionals and measure-valued generators of PDMPs

主 讲 人 ：刘国欣    教授

活动时间：05月26日10时30分    

地      点 ：数信学院D-203教室

讲座内容：

We consider apiecewise-deterministic Markov process (PDMP) with general conditionaldistribution of inter-occurrence time, which is called a general PDMP here. Ourpurpose is to establish the theory of measure-valued generator for generalPDMPs. The additive functional of a semi-dynamic system (SDS) is introduced firstly,which presents us an analytic tool for the whole paper. The additivefunctionals of a general PDMP are represented in terms of additive functionalsof the SDS. The necessary and sufficient conditions of being a local martingaleor a special semimartingale for them are given. The measure-valued generatorfor a general PDMP is introduced, which takes value in the space of additivefunctionals of the SDS. And its domain is completely described by analyticconditions. This domain is extended to the locally path-finite variationfunctions. As an application of measure-valued generator, we study the expectedcumulative discounted value of an additive functional of the general PDMP, andget a measure integro-differential equation satisfied by the expectedcumulative discounted value function.

主讲人介绍：

刘国欣，现任石家庄铁道大学副校长,教授、博导。长沙铁道学院概率论与数理统计专业博士。

上世纪90年代初主要从事概率论极限定理的研究工作，在非齐次马氏链泛函的强大数定律及条件三级数定理研究中取得了重要进展。1995年师从著名数学家侯振挺教授研究马氏骨架过程。获湖南省首届优秀博士论文奖。对马氏骨架过程中重要的一类----逐段决定马氏骨架过程的研究作了基础性的工作；为逐段决定马氏过程的研究奠定了全新的起点和新的理论基础。主要研究成果汇集于与侯振挺教授合著的专著《Markov Skeleton Processes and their Applications》。近年来，把研究重点转向保险风险问题驱动的逐段决定马氏过程理论的研究。主持并完成国家自然科学基金项目2项,现在研主持1项。在Stochastic Processes and their Application, Statistics andProbability Letters, Insurance: Mathematics and Economics, 中国科学等重要期刊发表论文30余篇，著作3部。2007年获天津市五一劳动奖章。现兼任中国工程概率统计学会理事长、河北省数学会理事长。

发布时间：2018-05-23 10:35:11