Two different ways of trimming the sample path of a stochastic process in D[0, 1]: global ("trim as you go") trimming and record time ("lookback") trimming are analysed to find conditions for the corresponding operators to be continuous with respect to the (strong) J 1 -topology. A key condition is that there should be no ties among the largest ordered jumps of the limit process. As an application of the theory, via the continuous mapping theorem we prove limit theorems for trimmed Lévy processes, using the functional convergence of the underlying process to a stable process. The results are applied to a reinsurance ruin time problem.

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In an exploratory quasi-experimental observational study, 138 participants recruited during a university orientation week were exposed to social engineering directives in the form of fake email or phishing attacks over several months in 2017. These email attacks attempted to elicit personal information from participants or entice them into clicking links which may have been compromised in a real-world setting. The study aimed to determine the risks of cybercrime for students by observing their responses to social engineering and exploring attitudes to cybercrime risks before and after the phishing phase. Three types of scam emails were distributed that varied in the degree of individualization: generic, tailored, and targeted or ‘spear.’ To differentiate participants on the basis of cybercrime awareness, participants in a ‘Hunter’ condition were primed throughout the study to remain vigilant to all scams, while participants in a ‘Passive’ condition received no such instruction. The study explored the influence of scam type, cybercrime awareness, gender, IT competence, and perceived Internet safety on susceptibility to email scams. Contrary to the hypotheses, none of these factors were associated with scam susceptibility. Although, tailored and individually crafted email scams were more likely to induce engagement than generic scams. Analysis of all the variables showed that international students and first year students were deceived by significantly more scams than domestic students and later year students. A Generalized Linear Model (GLM) analysis was undertaken to further explore the role of all the variables of interest and the results were consistent with the descriptive findings showing that student status (domestic compared to international) and year of study (first year student compared to students in second, third and later years of study) had a higher association to the risk of scam deception. Implications and future research directions are discussed.

When S = (S t ) t≥0 is an α-stable subordinator, the sequence of ordered jumps of S, up till time 1, omitting the r largest of them, and taken as proportions of their sum (r) S t , defines a 2-parameter distribution on the infinite dimensional simplex, ∇ ∞ , which we call the PD (r) α distribution. When r = 0 it reduces to the PD α distribution introduced by Kingman in 1975. We observe a serendipitous connection between PD (r) α and the negative binomial point process of Gregoire (1984), which we exploit to analyse in detail a size-biased version of PD (r) α . As a consequence we derive a stick-breaking representation for the process and a useful form for its distribution. This program produces a large new class of distributions available for a variety of modelling purposes.