Max-stable processes arise from an infinite-dimensional generalisation of extreme value theory. They form a natural class of processes when sample maxima are observed at each site of a spatial process, a problem of particular interest in connection with regional estimation methods in hydrology. A general representation of max-stable processes due to de Haan and Vatan is discussed, and examples ...

Definition 1 (Time Series). A time series is a sequence of observations ordered with respect to a time index t, taking values in an index set S. If the set S contains a finite or countable number of elements we speak of discrete-time time series and the generic observation is indicated with the symbol yt, while if S is a continuum we have a continuous-time time series, whose generic observation...

We characterize all stationary time reversible Markov processes whose finite dimensional marginal distributions (of all orders) are infinitely divisible– MISTI processes, for short. Aside from two degenerate cases (iid and constant), in both discrete and continuous time every such process with full support is a branching process with Poisson or Negative Binomial marginal univariate distribution...

Ontogenetic niche shifts occur across diverse taxonomic groups, and can have critical implications for population dynamics, community structure, and ecosystem function. In this study, we provide a hypothesis-testing framework combining univariate and multivariate analyses to examine ontogenetic niche shifts using stable isotope ratios. This framework is based on three distinct ontogenetic niche...

We are going to give necessary and suucient conditions for a multivariate stationary stochastic process to be completely regular. We also give the answer to a question of V.V. Peller concerning the spectral measure characterization of such processes .