Document Zbl 1164.60354

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Some properties of random Poisson sums with \(\phi\)-sub-Gaussian terms. (Ukrainian. English summary) Zbl 1164.60354

Prykl. Stat., Aktuarna Finans. Mat. 2007, No. 1, 133-148 (2007).

Summary: Poisson sums with \(\phi\)-sub-Gaussian random terms are investigated. Estimates of the probability of such sums to exceed a level, which is specified by a continuous monotone increasing function, are obtained. As an example, the obtained results are applied to sub-Gaussian risk processes.

MSC:

60G15	Gaussian processes
62P05	Applications of statistics to actuarial sciences and financial mathematics

Keywords:

random Poisson sum; \(\phi\)-sub-Gaussian random variable; probability of exceeding; risk process

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