：Exponential change of measure for general piecewise deterministic Markov processes论文

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作者（2019）在《Exponential change of measure for general piecewise deterministic Markov processes》一文中研究指出：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■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.

Abstract

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■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.

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