We continue a program generalizing classical results from the analysis on symmetric cones to Dunkl setting for root systems of type A A ...

We show how the Mellin transform can be used to derive differential criteria for integral representations of functions as scale mixtures, and apply this idea to derive differential criteria for positive definiteness of functions in a manner similar to that of Gneiting (1999,2001). We also give a simple derivation of Williamson’s result on multiply monotone functions (Williamson, 1956), with a l...

In the present paper, we consider Post-Widder operators and its modified form which preserve test function xr, r ∈ ℕ. We estimate direct results in terms of modulus continuity for operators. Also, some estimates polynomially bounded functions linear combinations are considered. Our improve sense previous original

Asian options paying the excess over strike, of either the arithmetic or geometric average of the asset price over either discrete or continuous time, are valued using analytical and simulation methodologies. Expressions are developed for the double Laplace transform of the continuous arithmetic Asian option in both its strike and maturity. Analytical option prices for the continuous arithmetic...

Hirschman and Widder introduced a class of Pólya frequency functions given by linear combinations one-sided exponential functions. The members this are probability densities, the is closed under convolution but not pointwise multiplication. We show that, generically, polynomial function such density only if homothety, also identify subclass for which each positive-integer power function. furthe...