Some Applications of the Mellin Transform in Statistics

Some Applications of the Mellin Transform to Asymptotics of Series

Mellin transforms are used to find asymptotic approximations for functions defined by series. Such approximations were needed in the analysis of a water-wave problem, namely, the trapping of waves by submerged plates. The method seems to have wider applicability.

Some Applications of the Mellin Transform to Branching Processes

We introduce a Mellin transform of functions which live on all of R and discuss its applications to the limiting theory of Bellman-Harris processes, and specifically Luria-Delbrück processes. More precisely, we calculate the life-time distribution of particles in a Bellman-Harris process from their first-generation offspring and limiting distributions, and prove a formula for the Laplace transf...

Note on fractional Mellin transform and applications.

In this article, we define the fractional Mellin transform by using Riemann-Liouville fractional integral operator and Caputo fractional derivative of order [Formula: see text] and study some of their properties. Further, some properties are extended to fractional way for Mellin transform.

The Twisted Mellin Transform

The “twisted Mellin transform” is a slightly modified version of the usual classical Mellin transform on L([0,∞)). In this short note we investigate some of its basic properties. From the point of view of combinatorics one of its most interesting properties is that it intertwines the differential operator, df/dx, with its finite difference analogue, ∇f = f(x)−f(x−1). From the point of view of a...

Generalized Product Theorem for the Mellin Transform and Its Applications