In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, howev...In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.展开更多
Recently, Clancy [SIR epidemic models with general infectious period distribution, Statist. Prob. Left. 85 （2014） 1-5] has shown how SIR epidemics in which individuals＇ infection periods are not necessarily exponen...Recently, Clancy [SIR epidemic models with general infectious period distribution, Statist. Prob. Left. 85 （2014） 1-5] has shown how SIR epidemics in which individuals＇ infection periods are not necessarily exponentially distributed may be modeled in terms of a piecewise-deterministic Markov process （PDMP）. In this paper, we present a more detailed description of the underlying PDMP, from which we analyze the population transmission number and the infection probability of a certain susceptible individual.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 10871102)National Basic Research Program of China (973 Program) 2007CB814905
文摘In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.
文摘Recently, Clancy [SIR epidemic models with general infectious period distribution, Statist. Prob. Left. 85 （2014） 1-5] has shown how SIR epidemics in which individuals＇ infection periods are not necessarily exponentially distributed may be modeled in terms of a piecewise-deterministic Markov process （PDMP）. In this paper, we present a more detailed description of the underlying PDMP, from which we analyze the population transmission number and the infection probability of a certain susceptible individual.
