Mellin convolutions, statistical distributions and fractional calculus
نویسندگان
چکیده
منابع مشابه
Fractional Calculus of Periodic Distributions
Two approaches for defining fractional derivatives of periodic distributions are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier series. The second is based on the Grünwald-Letnikov formula for defining a fractional derivative as a limit of a fractional difference quotie...
متن کاملStatistical aspects of the fractional stochastic calculus
We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by fractional Brownian motion with any level of Holder-regularity (any Hurst parameter...
متن کاملNote 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.
متن کاملSTATISTICAL DISTRIBUTIONS ON WORDS AND q-CALCULUS ON PERMUTATIONS
As for the symmetric group of ordinary permutations there is also a statistical study of the group of signed permutations, that consists of calculating multivariable generating functions for this group by statistics involving record values and the length function. Two approaches are here systematically explored, using the flag-major index on the one hand, and the flag-inversion number on the ot...
متن کاملConvolutions of long-tailed and subexponential distributions
We study convolutions of long-tailed and subexponential distributions (probability measures), and more general finite measures, on the real line. Our aim is to prove some important new results, and to do so through a simple, coherent and systematic approach. It turns out that all the standard properties of such convolutions are then obtained as easy consequences of these results. Thus we also h...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fractional Calculus and Applied Analysis
سال: 2018
ISSN: 1311-0454,1314-2224
DOI: 10.1515/fca-2018-0022