Visualizing data through Czekanowski’s diagram has as its aim the illus-tration of the relationships between objects. Often, obvious clusters of observationsare directly visible. However, it is not straightforward to precisely delineate theseclusters. This paper presents the development of the package RMaCzek, which nowincludes features for cluster identification in Czekanowski diagrams.

Many classical variables (statistics) are selfdecomposable.They admit the random integral representations via Lévy processes.In this note are given formulas for their background driving distribution functions (BDDF).This may be used for a simulation of those variables.Among the examples discussed are: gamma variables, hyperbolic characteristic functions, Student t-distributions, stochastic area under planar Brownian motions, inverse Gaussian variable, logistic distributions, non-central chi-square, Bessel densities and Fisher z-distributions.Found representations might be of use in statistical applications.

Under certain conditions, we establish explicit upper bounds for an investor's expected payoff on two stocks. The proof of these bounds is based on a certain optimal stopping problem and a pointwise estimate for solutions of a second-order elliptic equation.

We reconsider a one-dimensional probabilistic model of a re-induced tree-grass coexistence in savannas introduced by D'Odorico, Laio and Ridol in [5].We rewrite it as a logistic growth model with random tree biomass losses caused by re occurring at random times.We study it by using the stochastic semigroup theory and we give new sucient conditions for the existence and stability of a unique stationary density of woody biomass.