Characterization of spatial Poisson process along optional increasing paths. A problem of dimension's reduction (Q1962229)
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scientific article; zbMATH DE number 1395192
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Characterization of spatial Poisson process along optional increasing paths. A problem of dimension's reduction |
scientific article; zbMATH DE number 1395192 |
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Characterization of spatial Poisson process along optional increasing paths. A problem of dimension's reduction (English)
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1 February 2001
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The paper investigates the problem of dimension reduction of a plane Poisson process by considering this process along optional increasing paths (OIPs). A convenient characterization of the spatial Poisson process is obtained on the basis of a suitable reparametrization of an OIP that succeeds to transform the process along the path into a one-parameter Poisson process. The key idea within the proof of these results is based on similar facts that hold for one-parameter martingales stopped by a family of bounded stopping times.
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martingales
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plane Poisson process
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dimension reduction
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optimal increasing path
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bounded stopping times
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