This paper addresses the problem of estimating the tail index Α of distributions with heavy, Pareto-type tails for dependent data, that is of interest in the areas of finance, insurance, environmental monitoring and teletraffic analysis. A novel approach based on the max self-similarity scaling...

We address the notion of association of sum- and max-stable processes from the perspective of linear and max-linear isometries. We establish the appealing result that these two classes of isometries can be identified on a proper space (the extended positive ratio space). This yields a natural...

The multifractional Brownian motion (MBM) processes are locally self-similar Gaussian processes. They extend the classical fractional Brownian motion processes by allowing their self-similarity parameter H[set membership, variant](0,1) to depend on time. Two types of MBM processes were...

We characterize all possible independent symmetric α-stable (SαS) components of an SαS process, 0<α<2. In particular, we focus on stationary SαS processes and their independent stationary SαS components. We also develop a parallel characterization theory for max-stable processes.