For a zero-mean, unit-variance stationary univariate Gaussian process we derive the probability that a record at the time n, say $X_n$ , takes place, and derive its distribution function. We study the joint distribution of the arrival time process of records and the distribution of the increments between records. We compute the expected number of records. We also consider two consecutive and non-consecutive records, one at time j and one at time n, and we derive the probability that the joint records $(X_j,X_n)$ occur, as well as their distribution function. The probability that the records $X_n$ and $(X_j,X_n)$ take place and the arrival time of the nth record are independent of the marginal distribution function, provided that it is continuous. These results actually hold for a strictly stationary process with Gaussian copulas.

It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We extend this result to higher dimensions by considering copulas. We show that the strong convergence result holds for copulas that are in a differential neighbourhood of a multivariate generalised Pareto copula. Sklar’s theorem then implies convergence in variational distance of the maximum of n independent and identically distributed random vectors with arbitrary common distribution function and (under conditions on the marginals) of its appropriately normalised version. We illustrate how these convergence results can be exploited to establish the almost-sure consistency of some estimation procedures for max-stable models, using sample maxima.

Consider a random vector $\textbf{U}$ whose distribution function coincides in its upper tail with that of an Archimedean copula. We report the fact that the conditional distribution of $\textbf{U}$ , conditional on one of its components, has under a mild condition on the generator function independent upper tails, no matter what the unconditional tail behavior is. This finding is extended to Archimax copulas.

In light of growing demand and pollution versus a finite amount of resources, electronic waste recycling is a way towards material circularity. New recycling technologies not only face technical difficulties but also need to overcome challenges of feasibility in both economic and environmental aspects. An assessment regarding environmental impacts and economic factors at the early development stages of such technologies is necessary to ensure a successful establishment. A batch lab-scale process using bioleaching to win indium from electronic waste was drafted using recent research in the field. Life Cycle Assessment (LCA) was used to determine the environmental impacts in four different categories at the lowest Technology Readiness Level (TRL). The findings were then compared to two existing chemical leaching processes to put them in perspective. Results show that the electricity consumption is the major contribution to environmental impacts. The assumed bioleaching process has a higher environmental impact than the two chemical processes due to its high duration and resulting high electricity consumption. However, the research has also proven, that an LCA during the conceptual phase has a high uncertainty due to lack of data and knowledge about the process.

Reduced absorption capacity in patients with intestinal resections (IR) could result in malabsorption of fat-soluble components like carotenoids, which are of clinical interest in relation to visual health. In this case cohort, we investigated the association between IR and serum lutein, zeaxanthin, β-carotene and macular pigment optical density, when compared with healthy controls. Ten patients with IR and twelve healthy controls were included in the study. Baseline characteristics were comparable between groups, except for higher serum TAG (P < 0·05) and shorter bowel length (P < 0·0001) in the group with IR. Serum lutein, zeaxanthin, β-carotene and macular pigment optical density were >15 % lower in the patient group compared with healthy controls (P < 0·05, adjusted for age) and, in the case of serum lutein and zeaxanthin, also for dietary intake of carotenoids. Results suggest that for a test of macular carotenoid supplementation, subjects with a potentially clinically significant carotenoid deficit could be recruited among patients with IR.

In practice, it is not possible to observe a whole max-stable random field. Therefore, we propose a method to reconstruct a max-stable random field in C([0, 1]k) by interpolating its realizations at finitely many points. The resulting interpolating process is again a max-stable random field. This approach uses a generalized max-linear model. Promising results have been established in the k = 1 case of Falk et al. (2015). However, the extension to higher dimensions is not straightforward since we lose the natural order of the index space.

We propose a method to generate a max-stable process in C[0, 1] from a max-stable random vector in Rd by generalizing the max-linear model established by Wang and Stoev (2011). For this purpose, an interpolation technique that preserves max-stability is proposed. It turns out that if the random vector follows some finite-dimensional distribution of some initial max-stable process, the approximating processes converge uniformly to the original process and the pointwise mean-squared error can be represented in a closed form. The obtained results carry over to the case of generalized Pareto processes. The introduced method enables the reconstruction of the initial process only from a finite set of observation points and, thus, a reasonable prediction of max-stable processes in space becomes possible. A possible extension to arbitrary dimensions is outlined.