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

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.


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