Results 1 to 10 of about 102 (99)

Some class of nonlinear partial differential equations in the ring of copolynomials over a commutative ring [PDF]

Frontiers in Applied Mathematics and Statistics
We study the copolynomials, i.e., K-linear mappings from the ring of polynomials K[x] into the commutative ring K. With the help of the Cauchy–Stieltjes transform of a copolynomial, we introduce and examine a multiplication of copolynomials.
Sergiy L. Gefter, Aleksey L. Piven'
doaj   +3 more sources

Averages for Multivariate Random Vectors with Random Weights

Revstat Statistical Journal, 2020
We consider a random weights average of n independent continuous random vectors X1, ..., Xn, where random weights are cuts of [0, 1] by an increasing sequence of the order statistics of a random sample from a uniform [0, 1].
A.R. Soltani , Rasool Roozegar
doaj   +1 more source

Central limit measure for V-monotone independence

, 2023
We study the central limit distribution $\mu$ for V-monotone independence. Using its Cauchy--Stieltjes transform, we prove that $\mu$ is absolutely continuous with respect to the Lebesgue measure on $\mathbb{R}$ and we give its density $\rho$ in an ...
Dacko, Adrian
core   +1 more source

Some Limiting Laws in Non-Commutative Probability

Axioms
In this article, we provide some new limiting laws related to the free multiplicative law of large numbers and involving free and Boolean additive convolutions.
Ayed. R. A. Alanzi, Raouf Fakhfakh, Fatimah Alshahrani   +2 more
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FOURIER AND CAUCHY–STIELTJES TRANSFORMS OF POWER LAWS INCLUDING STABLE DISTRIBUTIONS

, 2012
We introduce a class of probability measures whose densities near infinity are mixtures of Pareto distributions. This class can be characterized by the Fourier transform which has a power series expansion including real powers, not only integer powers ...
TAKAHIRO HASEBE
core   +1 more source

A Generalized Framework for the (a, b)-Transformation of Probability Measures

Mathematics
In this paper, we propose an analytic deformation acting on probability measures, designed to encompass and extend two fundamental operators in free probability: the (a,b)- and the Tc-deformations.
Raouf Fakhfakh, Ghadah Alomani, Abdulmajeed Albarrak   +2 more
doaj   +1 more source

Studies on the Marchenko–Pastur Law

Mathematics
In free probability, the theory of Cauchy–Stieltjes Kernel (CSK) families has recently been introduced. This theory is about a set of probability measures defined using the Cauchy kernel similarly to natural exponential families in classical probability ...
Ayed. R. A. Alanzi, Ohud A. Alqasem, Maysaa Elmahi Abd Elwahab, Raouf Fakhfakh   +3 more
doaj   +1 more source

SOME GEOMETRIC PROPERTIES OF THE SUBORDINATION FUNCTION ASSOCIATED TO AN OPERATOR-VALUED FREE CONVOLUTION SEMIGROUP

, 2019
Latex, 20 pages, version extended to study Julia-Caratheodory derivatives for the functions involved.International audienceIn his article ''On the free convolution with a semicircular distribution," Biane found very useful characterizations of the ...
Belinschi, Serban, Belinschi, Serban Teodor   +1 more
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On Generalized V_a-Transformation of Measures

Mathematics
In this study, we introduce a novel transformation of probability measures that unifies two significant transformations in free probability theory: the t-transformation and the Va-transformation.
Abdulmajeed Albarrak, Raouf Fakhfakh, Ghadah Alomani   +2 more
doaj   +1 more source

Some Results on the Free Poisson Distribution

Axioms
Let K+(μi)={Qsiμi,si∈(m0μi,m+μi)}, i=1,2, be two CSK families generated by the nondegenerate probability measures μ1 and μ2 with support bounded from above.
Ayed. R. A. Alanzi, Ohud A. Alqasem, Maysaa Elmahi Abd Elwahab, Raouf Fakhfakh   +3 more
doaj   +1 more source