de Vylder, F. Compound and mixed distributions. (English) Zbl 0666.60016 Insur. Math. Econ. 8, No. 1, 57-62 (1989). We investigate compound distributions, mixed distributions and relations between them. As applications we show how some results on infinite divisibility are easily obtained and we prove a theorem stating that any stochastic process on [0,\(\infty)\) with increasing trajectories vanishing in a neighbourhood of the origin and with stationary and independent increments is necessarily compound Poisson distributed. Cited in 1 Document MSC: 60E05 Probability distributions: general theory 60E07 Infinitely divisible distributions; stable distributions Keywords:compound distributions; mixed distributions; infinite divisibility; compound Poisson distributed PDFBibTeX XMLCite \textit{F. de Vylder}, Insur. Math. Econ. 8, No. 1, 57--62 (1989; Zbl 0666.60016) Full Text: DOI References: [1] Feller, W., An Introduction to Probability Theory and Its Applications, VolumeI (1960), Wiley: Wiley New York · Zbl 0138.10207 [2] Feller, W., An Introduction to Probability Theory and Its Applications, Volume II (1966), Wiley: Wiley New York · Zbl 0138.10207 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.