Poisson-type functional limit theorem for the measure of union of random sets (Q2726274)
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scientific article; zbMATH DE number 1620711
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Poisson-type functional limit theorem for the measure of union of random sets |
scientific article; zbMATH DE number 1620711 |
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16 July 2001
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random set
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convergence
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Doléans equation
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Poisson measure
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Poisson-type functional limit theorem for the measure of union of random sets (English)
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A model covering the plane by disks with random radii and centers is considered. It is proved that the radian measure of the covered region converges to the solution of a Doléans equation with jumps. The proof of the result is based upon the martingale criterion for convergence to a solution of a stochastic differential equation and is contained in the previous paper of the author [Theory Probab. Math. Stat. 57, 181-186 (1998); translation from Teor. Jmovirn. Mat. Stat. 57, 168-173 (1997; Zbl 0939.60034)]. A geometrical illustration to the result is also considered.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00022].
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