63 research outputs found
Moment Determinacy of Powers and Products of Nonnegative Random Variables
We find conditions which guarantee moment (in)determinacy of powers and
products of nonnegative random variables. We establish new and general results
which are based either on the rate of growth of the moments of a random
variable or on conditions about the distribution itself. For the class of
generalized gamma random variables we show that the power and the product of
such variables share the same moment determinacy property. A similar statement
holds for half-logistic random variables. Besides answering new questions in
this area, we either extend some previously known results or provide new and
transparent proofs of existing results
Integral Representations of Three Novel Multiple Zeta Functions for Barnes Type: A Probabilistic Approach
Integral representation is one of the powerful tools for studying analytic
continuation of the zeta functions. It is known that Hurwitz zeta function
generalizes the famous Riemann zeta function which plays an important role in
analytic number theory. They both have several multiple versions in the
literature. In this paper, we introduce three novel multiple zeta functions for
Barnes type and study their integral representations through hyperbolic
probability distributions given by Pitman and Yor (2003, Canad. J. Math., 55,
292-330). The analytically continued properties of the three multiple zeta
functions are also investigated. Surprisingly, two of them, unlike the previous
results, can extend analytically to entire functions in the whole complex
plane.Comment: 20 page
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