Martingale characterization of Pólya processes and sequences (Q946016)
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scientific article; zbMATH DE number 5345541
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Martingale characterization of Pólya processes and sequences |
scientific article; zbMATH DE number 5345541 |
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Martingale characterization of Pólya processes and sequences (English)
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22 September 2008
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The author proves that a mixed Poisson process \(\xi=(\xi_t)_{t\geq0}\) is a Pólya process if and only if there exists a non-degenerate linear transformation \(\xi_t\mapsto\eta_t=a(t)\xi_t+b(t)\) such that \(\eta=(\eta_t)_{t\geq0}\) is a martingale. This martingale characterization provides an optimal forecast for the value of the random variable \(\xi_T\). An analogous result is proved for Pólya sequences.
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Pólya processes
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Pólya sequences
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martingales
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Poisson processes
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0.9446624
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0.90664715
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0.90027785
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0.8961377
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0.8871833
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0.8775341
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