“Mixed Poisson process”的意思、由来-开放百科全书

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Mixed Poisson process

释义

Definition
Comment
Properties
Sources

In probability theory, a mixed Poisson process is a special point process that is a generalization of a Poisson process. Mixed Poisson processes are simple example for Cox processes.

Definition

Let be a locally finite measure on and let be a random variable with almost surely.

Then a random measure on is called a mixed Poisson process based on and iff conditionally on is a Poisson process on with intensity measure .

Comment

Mixed Poisson processes are doubly stochastic in the sense that in a first step, the value of the random variable is determined. This value then determines the "second order stochasticity" by increasing or decreasing the original intensity measure .

Properties

Conditional on mixed Poisson processes have the intensity measure and the Laplace transform

.

Sources

{{cite book |last1=Kallenberg |first1=Olav |author-link1=Olav Kallenberg |year=2017 |title=Random Measures, Theory and Applications|location= Switzerland |publisher=Springer |doi= 10.1007/978-3-319-41598-7|isbn=978-3-319-41596-3}}

1 : Poisson point processes

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