This paper investigates the nature of the physical processes underlying the origin of the Ion Cyclotron Waves (ICWs) and Kinetic Alfvén Waves (KAWs) in the solar wind, by studying their Waiting Time Distributions (WTDs). The results show that ICWs and KAWs do not share common statistical properties: while KAWs independently occur as stochastic, uncorrelated wave packets governed by Poisson statistics, ICWs are highly correlated, thus departing from the Poisson hypothesis. The results based on

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... e WTD analysis may cast more light on the mechanisms actively at work in the generation of the two wave modes. Specifically, while the stochastic character of KAWs may be reminiscent of the random convection-driven jostling of the flux-tube foot-points that generates the Alfvén waves in the lower solar atmosphere, the correlations among the ICW events can be effectively explained on the basis of the persistent nature of the mechanism underlying the local origin of ICWs, namely the proton cyclotron instability. Alternative explanations for the observed distribution of ICW waiting times, based on a piecewise-constant Poisson process involving time-varying rates, are also reported.