Välkommen till föreläsningen i seminarieserien i matematik.
Due to their flexibility, Fox-H functions are widely studied and applied to
many research topics, such as physics, statistics, viscoelasticity, etc. The special cases
represented by the Mittag-Leffler and Wright functions prove their great impact. In
this talk, we focus on certain explicit assumptions that allow us to use the Fox-H
functions as densities. We then provide a subfamily of the latter, called Fox-H densities
with moments of any order, and give their Laplace transforms as entire generalized
Wright functions. The class of r.v.’s with these densities is proved to possess a monoid
structure. We present eight subclasses of special cases of such densities (together with
their Laplace transforms) that are particularly relevant in applications. To analyze the
existence conditions of Fox-H functions, we derive asymptotic results and their analytic
extension.