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Related papers: Moment formulae for general point processes

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We present new exact expressions for a class of moments for the geometric Brownian motion, in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Ito's Wiener process. We then apply the…

Statistical Mechanics · Physics 2022-09-13 Francesco Caravelli , Toufik Mansour , Lorenzo Sindoni , Simone Severini

Gaussian mixture models are universal approximators in the sense that any smooth density can be approximated arbitrarily well with a Gaussian mixture model with enough components. Due to their broad expressive power, Gaussian mixture models…

Computation · Statistics 2025-02-12 Haley Colgate Kottler , Julia Lindberg , Jose Israel Rodriguez

We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…

Statistics Theory · Mathematics 2012-01-17 Daniel M. Packwood

We derive a recursive formula for the moments of the number of flips using a possibly biased coin to produce a prescribed finite binary string $S$ when $S$ is either a run of heads or a run of heads followed by a tails. Our recursive…

Combinatorics · Mathematics 2026-05-20 Jia Huang

Given a uniform ensemble of quantum density matrices $\rho$, it is useful to calculate the mean value over this ensemble of a product of entries of $\rho$. We show how to calculate such moments in this paper. The answer involves well known…

Quantum Physics · Physics 2007-05-23 Robert R. Tucci

We develop the generalized method of moments (GMM) estimation for the parameters of the finitely mixed multi-mixed fractional Ornstein--Uhlenbeck (mmfOU) processes, and analyze the consistency and asymptotic normality of this estimator. We…

Statistics Theory · Mathematics 2024-01-11 Hamidreza Maleki Almani , Tommi Sottinen

A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…

Statistical Mechanics · Physics 2015-05-20 Baruch Barzel , Ofer Biham

Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…

Methodology · Statistics 2015-03-17 Joan Bruna , Stéphane Mallat , Emmanuel Bacry , Jean-François Muzy

We propose Mecke-Palm formulas for multiple integrals with respect to a Poisson random measure interlaced with its intensity measure. We apply such formulas to multiple mixed L\'evy systems of L\'evy processes and obtain moment formulas for…

Probability · Mathematics 2016-06-14 Krzysztof Bogdan , Jan Rosiński , Grzegorz Serafin , Łukasz Wojciechowski

The purpose of the present paper is to establish moment estimates of Rosenthal type for a rather general class of random variables satisfying certain bounds on the cumulants. We consider sequences of random variables which satisfy a central…

Probability · Mathematics 2019-01-16 Peter Eichelsbacher , Lukas Knichel

We use nowdays classical theory of generalized moment problems by Krein-Nudelman [1977] to define a special class of stochastic Gaussian processes. The class contains, of course, stationary Gaussian processes. We obtain a spectral…

Spectral Theory · Mathematics 2010-08-04 L. Baratchart , L. Golinskii , S. Kupin

In this paper, we generalise the formula for the fourth moment of a random determinant to account for entries with asymmetric distribution. We also derive the second moment of a random Gram determinant.

Probability · Mathematics 2023-09-25 Dominik Beck

In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…

Probability · Mathematics 2012-02-09 Alexander Goldenshluger , Oleg Lepski

Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on the knowledge of the behavior of the…

Analysis of PDEs · Mathematics 2021-11-01 Alberto Lastra , Sławomir Michalik , Maria Suwińska

Recursions for moments of multi-type continuous state and continuous time branching process with immigration are derived. It turns out that the $k$-th (mixed) moments and the $k$-th (mixed) central moments are polynomials of the initial…

Probability · Mathematics 2018-01-19 Matyas Barczy , Zenghu Li , Gyula Pap

We first derive the recurisions for integer moments of two-type continuous-state branching processes in L\'{e}vy random environments. Result shows that the $n$th moment of the process is a polynomial of the initial value of the process with…

Probability · Mathematics 2022-08-05 Shukai Chen , Xiangqi Zheng

The maximum composite likelihood estimator for parametric models of determinantal point processes (DPPs) is discussed. Since the joint intensities of these point processes are given by determinant of positive definite kernels, we have the…

Statistics Theory · Mathematics 2019-09-04 Kou Fujimori , Sota Sakamoto , Yasutaka Shimizu

We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…

Number Theory · Mathematics 2025-12-16 Jean-François Burnol

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…

Information Theory · Computer Science 2020-07-15 Neri Merhav , Igal Sason

In the study of the amplitudes for many-particle processes, and also for processes involving particles with spin, the use is made of matrix elements of the rotation group d^j_{\mu\nu}(z). In this paper the generalization of the functions…

Mathematical Physics · Physics 2014-05-16 Ya. I. Azimov