Exponential change of measure for general piecewise deterministic Markov processes

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（4）
• 页码范围: 719-734
• 页数: 16页
• 语种: 英文

摘要

We consider a general piecewise deterministic Markov process (PDMP) X ={Xt}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 Mft=f(Xt)/f(X0)[Sexp(∫(0,t)dL(Af)s/f(Xs-))]-1By 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.