• Corpus ID: 248887261

Renormalization of divergent moment in probability theory

@inproceedings{Zhang2022RenormalizationOD,
  title={Renormalization of divergent moment in probability theory},
  author={Ping Zhang and Wen-Du Li and Wu-Sheng Dai},
  year={2022}
}
: Some probability distributions have moments, and some do not. For example, the normal distribution has power moments of arbitrary order, but the Cauchy distribution does not have power moments. In this paper, by analogy with the renormalization method in quantum field theory, we suggest a renormalization scheme to remove the divergence in divergent moments. We establish more than one renormalization procedure to renormalize the same moment to prove that the renormalized moment is scheme… 

References

SHOWING 1-10 OF 41 REFERENCES
The number of eigenstates: counting function and heat kernel
The main aim of this paper is twofold: (1) revealing a relation between the counting function N(lambda) (the number of the eigenstates with eigenvalue smaller than a given number) and the heat kernel
Introduction to Second Kind Statistics: Application of Log-Moments and Log-Cumulants to the Analysis of Radar Image Distributions
Statistical methods classically used to analyse a probability density function (pdf) are founded on the Fourier transform, on which useful tools such the first and second characteristic function are
Scaling behavior of the momentum distribution of a quantum Coulomb system in a confining potential
We calculate the single-particle momentum distribution of a quantum many-particle system in the presence of the Coulomb interaction and a confining potential. The region of intermediate momenta,
Fractional calculus: an introduction for physicists, 3rd edition
Fractional Calculus can be viewed as extending the concept of an ‘nth-order derivative’ from the integers (‘n’ is an integer) to an ‘α-th’ order derivative, where ‘α’ is a real number, complex
Why Lévy α-stable distributions lack general closed-form expressions for arbitrary α.
TLDR
It is argued that there cannot be closed-form expressions in terms of elementary functions for p_{ α}(x) for general α because of the complete complex analytic structure of p_{α}(z) using domain coloring.
An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions
In this paper, we provide an approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions and discuss the application of this approach in some physical
Truncated Lévy motion through path integrals and applications to nondiffusive suprathermal ion transport.
TLDR
The approach to treat tempered Lévy distributions is generalized and the model now recovers exponentially tempered tails above a chosen scale in the propagator and diffusion equation of truncated asymmetrical fractional Levy motion via path integrals.
Hilbert Space Geometry of Random Matrix Eigenstates.
TLDR
The Hilbert space geometry of eigenstates of parameter-dependent random matrix ensembles is discussed, deriving the full probability distribution of the quantum geometric tensor for the Gaussian unitary ensemble and the exact joint distribution function of the Fubini-Study metric and the Berry curvature is given.
Quantum electrodynamics : a bridge between mathematicians and physicists
Part I. Introduction.- Prologue.- 1. Mathematical Principles of Modern Natural Philosophy.- 2. The Basic Strategy of Extracting Finite Information from Infinities -- Ariadne's Thread in
...
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