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The permanental process. (English) Zbl 1126.60040

Summary: We extend the boson process first to a large class of Cox processes and second to an even larger class of infinitely divisible point processes. Density and moment results are studied in detail. These results are obtained in closed form as weighted permanents, so the extension is called a permanental process. Temporal extensions and a particularly tractable case of the permanental process are also studied. Extensions of the fermion process along similar lines, leading to so-called determinantal processes, are discussed.

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60K99 Special processes

Software:

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