Results 21 to 30 of about 102 (99)
A Common Generalization of the (a,b)- and (s,t)-Transformations of Probability Measures
AxiomsThis paper presents two analytic mappings defined on probability measures that extend and unify the (a,b)- and (s,t)-deformations arising in free probability for s, b>0 and a, t∈R.
Ghadah Alomani, Raouf Fakhfakh
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Functionals of Dirichlet processes, the Cifarelli-Regazzini identity and Beta-Gamma processes
, 2005 Suppose that P θ(g) is a linear functional of a Dirichlet process with shape θ H, where θ > 0 is the total mass and H is a fixed probability measure.
James, Lancelot F.
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.In this paper, we develop a comprehensive analytical framework for generalized nonlinear, nonhomogeneous Volterra integral equations and fractional differential equations in b‐metric spaces equipped with amorphous binary relations. By introducing an enriched (f, ϕ, ψ, s)‐functional contraction, we extend classical contractive conditions to accommodate ...
D. Srinivasan +2 more
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On
MathematicsThe concept of the (T=(s,t))-transformation of probability measures, introduced for s>0 and t∈R, is examined in this work from the perspective of Cauchy–Stieltjes kernel (CSK) families and their related variance functions (VFs).
Shokrya S. Alshqaq +2 more
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Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
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Stability of Cauchy–Stieltjes Kernel Families by Free and Boolean Convolutions Product
MathematicsLet F(νj)={Qmjνj,mj∈(m−νj,m+νj)}, j=1,2, be two Cauchy–Stieltjes Kernel (CSK) families induced by non-degenerate compactly supported probability measures ν1 and ν2. Introduce the set of measures F=F(ν1)⊞F(ν2)={Qm1ν1⊞Qm2ν2,m1∈(m−ν1,m+ν1)andm2∈(m−ν2,m+ν2)}.
Ayed. R. A. Alanzi +2 more
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On the t-Transformation of Free Convolution
MathematicsThe study of the stability of measure families under measure transformations, as well as the accompanying limit theorems, is motivated by both fundamental and applied probability theory and dynamical systems. Stability analysis tries to uncover invariant
Shokrya S. Alshqaq +2 more
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Nonlinear shrinkage test on a large‐dimensional covariance matrix
Statistica Neerlandica, Volume 79, Issue 1, February 2025.This paper is concerned with deriving a new test on a covariance matrix which is based on its nonlinear shrinkage estimator. The distribution of the test statistic is deduced under the null hypothesis in the large‐dimensional setting, that is, when p/n→c∈(0,+∞) with p variables and n samples both tending to infinity.
Taras Bodnar +2 more
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Notes on the Free Additive Convolution
AxiomsThe investigation of free additive convolution is a key concept in free probability theory, offering a framework for studying the sum of freely independent random variables.
Shokrya S. Alshqaq +2 more
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International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.For the Weinstein Laplacian considered on the Hilbert space which makes it a self‐adjoint operator, the Von Neumann spectral decomposition is given. As applications, a new integral representation for the Weinstein heat kernel is given. Also, it is proved that the spectrum of the semigroup associated with the Weinstein Laplacian is reduced to its ...
Abdelilah El Mourni +3 more
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