The Distribution of the Interval between Events of a Cox Process with Shot Noise Intensity | Zendy

Angelos Dassios | Zendy; Jiwook Jang | Zendy

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The Distribution of the Interval between Events of a Cox Process with Shot Noise Intensity

Author(s) -

Angelos Dassios,

Jiwook Jang

Publication year - 2008

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2008/367170

Subject(s) - cox process , shot noise , mathematics , laplace transform , piecewise , noise (video) , laplace distribution , intensity (physics) , statistical physics , statistics , mathematical analysis , computer science , artificial intelligence , image (mathematics) , physics , telecommunications , quantum mechanics , detector , poisson distribution , poisson process

Applying the piecewise derteministic processes theory, the probability generating function of a Cox process, incorporating with shot noise process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise process at claim jump times, using stationary assumption of the shot noise process at any times. Based on this Laplace transform and from the probability generating function of a Cox process with shot noise intensity, we obtain the distribution of the interval of a Cox process with shot noise intensity for insurance claims and its moments, that is, mean and variance.14 page(s

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