We develop a general probabilistic approach that enables one to get sharp estimates for the almost-sure short-term behavior of hierarchically structured branching-diffusion processes. This approach involves the thorough investigation of the cluster structure and the derivation of some...

We obtain exact almost-sure estimates for the short-time propagation of the closed support of (2, d, [beta])-superprocesses. Upper estimates are derived by solving a certain singular non-linear evolution equation, whereas lower estimates are obtained by the use of the branching-particle-system...

We delineate a connection of Kendall-Ressel and related laws with the lower real branch of Lambert W function. A characterization of the canonical member of Kendall-Ressel class is found. The Letac-Mora interpretation of the reciprocity of two specific NEFs is extended by considering two related...

We investigate two related classes of Poisson mixtures which comprise exponential dispersion models. The first one is constructed starting from a law related to Bachelier's work. Certain members of this model emerge in the gambler's ruin problem. The other model is comprised of the distributions...