Exponential change of measure for general piecewise deterministic Markov processes

作     者：Zhaoyang Liu Yuying Liu Guoxin Liu 

作者机构：School of Mathematics and Statistics Central South University Department of Mathematics and Physics Shijiazhuang Tiedao University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2019年第62卷第4期

页      面：719-734页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No. 11471218) Hebei Higher School Science and Technology Research Projects (Grant No. ZD20131017) 

主　　题：exponential change of measure piecewise deterministic Markov process measure-valued generator Stieltjes exponential 

摘      要：We consider a general piecewise deterministic Markov process(PDMP) X = {X_t}_(t≥0) with a measure-valued generator A, for which the conditional distribution function of the inter-occurrence time is not necessarily absolutely continuous. A general form of the exponential martingales that are associated with X is given by■By considering this exponential martingale to be a likelihood-ratio process, we define a new probability measure and show that the process X is still a general PDMP under the new probability measure. We additionally find the new measure-valued generator and its domain. To illustrate our results, we investigate the continuous-time compound binomial model.