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Seminarium i matematik

Fox-H densities and completely monotone generalized Wright functions

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.

D0070 Lorenzo Cristafano,University of Luxemburg, Luxemburg Lägg till i din kalender