Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a stable process while, in long time, it approximates another stable (possibly Gaussian) process. We also investigate the absolute continuity of a layered stable p...

We introduce and showcase [mvpd](https://CRAN.R-project.org/package=mvpd) (an acronym for *m*ulti*v*ariate *p*roduct *d*istributions), a package that uses product distribution approach to calculating multivariate subgaussian stable functions. The family of distributions are elliptically contoured contain the Cauchy normal distribution. These can be useful in modeling data phenomena have heavier...

This paper deals with measurable stationary symmetric stable random fields indexed by R and their relationship with the ergodic theory of nonsingular R-actions. Based on the phenomenal work of Rosiński (2000), we establish extensions of some structure results of stationary SαS processes to SαS fields. Depending on the ergodic theoretical nature of the underlying action, we observe different beh...

A stochastic process X is strongly stationary if its fdds are invariant under time shifts, that is, for any (finite) n, for any t0 and for all t1, ..., tn ∈ T , (Xt1 , ..., Xtn) and (Xt1+t0 , ..., Xtn+t0) have the same distribution. A stochastic process X is weakly stationary if its mean function is constant and its covariance function is invariant under time shifts. That is, for all t ∈ T , E(...