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| ON THE STRUCTURES OF RANDOM MEASURE AND POINT PROCESSCONVOLUTION SEMIGROUPS |
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Citation： |
He Yuanjiang.ON THE STRUCTURES OF RANDOM MEASURE AND POINT PROCESSCONVOLUTION SEMIGROUPS[J].Chinese Annals of Mathematics B,1996,17(4):467~476 |
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Net amount： 837 |
Authors： |
He Yuanjiang; |
Foundation： |
the National Natural Science Foundation of China and the Guangdong Provincial Natural Science |
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| Abstract： |
Let ${\bold D}$ be a convolution semigroup of random
measures or point processes on a locally compact second countable $T_2$ space. There is a topological isomorphism from ${\bold D}$ into a subsemigroup of product topological semigroup $({\bold R}_+,+)^{\bold N}$. ${\bold D}$ is a sequentially stable and $D$-separable ZH-semigroup, as well
as a metrizable, stable and normable Hun semigroup, so it has the corresponding properties. In particular the author has a new and simple proof by ZH-semigroup approach or Hun semigroup approach to show that ${\bold D}$ has property ILID (an infinitesimal array limit is infinitely divisible), and know the Baire types which some subsets of ${\bold D}$ belong in. |
Keywords： |
Random measure, Point process, ZH-semigroup, Hun semigroup, Property ILID |
Classification： |
60G55, 60G57 |
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