Modern Theory of Summation of Random Variables

DOI10.1515/9783110936537zbMath0907.60001OpenAlexW625718394MaRDI QIDQ4210937

Publication date: 9 September 1998

Full work available at URL: https://doi.org/10.1515/9783110936537

Infinitely divisible distributions; stable distributions (60E07) Research exposition (monographs, survey articles) pertaining to probability theory (60-02) Limit theorems in probability theory (60Fxx)

Related Items (69)

The best constant in the Rosenthal inequality for nonnegative random variables ⋮ Bounds for convergence rate in laws of large numbers for mixed Poisson random sums ⋮ Bounds of the accuracy of the normal approximation to the distributions of random sums under relaxed moment conditions ⋮ An efficient series approximation for the Lévy \(\alpha\)-stable symmetric distribution ⋮ Central limit theorems for solutions of the Kac equation: speed of approach to equilibrium in weak metrics ⋮ Optimal transportation and the falsifiability of incompletely specified economic models ⋮ On the rate of convergence to bivariate stable laws ⋮ On convergence of the distributions of random sequences with independent random indexes to variance–mean mixtures ⋮ Limit theorems for sums of heavy-tailed variables with random dependent weights ⋮ Diffusion approximation of systems with weakly ergodic Markov perturbations. I ⋮ Diffusion approximation of systems with weakly ergodic Markov perturbations. II ⋮ Asymptotical behavior of linear congruential generators ⋮ Wasserstein and total variation distance between marginals of Lévy processes ⋮ The law of large numbers in a metric space with a convex combination operation ⋮ Convergence in distribution norms in the CLT for non identical distributed random variables ⋮ Normal limiting distribution of the size of binary interval trees ⋮ Limit theorems for continuous-time random walks in the double-array limit scheme ⋮ Optimal rates of convergence of second-degree polynomials in several metrics ⋮ On the accuracy of approximation of the complex exponential by the first terms of its Taylor expansion and applications to the Fourier-Stieltjes transform ⋮ Quantitative and qualitative limits for exponential asymptotics of hitting times for birth-and-death chains in a scheme of series ⋮ On the stability of characterizations by an identical distribution property ⋮ On weak convergence of quasi-infinitely divisible laws ⋮ Asymptotically optimal Berry-Esseen-type bounds for distributions with an absolutely continuous part ⋮ Stochastic operation induced by group allocation of particles and generalized branching processes ⋮ In Memory of V. M. Zolotarev (02.27.1931--11.07.2019) ⋮ On the stability of mixtures of probability distributions to perturbations of mixing distributions ⋮ Resampling approach for cluster model selection ⋮ On normal variance-mean mixtures as limit laws for statistics with random sample sizes ⋮ Some optimal bounds in the central limit theorem using zero biasing ⋮ Asymptotic expansions in the CLT containing the last known moment in the main part ⋮ Possibility of recovering message segments based on side information about original characters ⋮ Spectral representations of characteristic functions of discrete probability laws ⋮ Copulas: Tales and facts (with discussion) ⋮ On the convergence of distributions of statistics constructed from samples of random size to a multivariate generalized variance-gamma distributions ⋮ Bounds for the Concentration Functions of Random Sums under Relaxed Moment Conditions ⋮ Characteristic functions and compactness of distributions of sums of independent random variables ⋮ Self-similar solutions in one-dimensional kinetic models: a probabilistic view ⋮ Goodness-of-fit tests based on the distance between the Dirichlet process and its base measure ⋮ Some aspects of decision making under uncertainty ⋮ On a non-classical invariance principle ⋮ Criteria of Relative and Stochastic Compactness for Distributions of Sums of Independent Random Variables ⋮ Convergence Rate Estimates in the Global CLT for Compound Mixed Poisson Distributions ⋮ Reaching the best possible rate of convergence to equilibrium for solutions of Kac's equation via central limit theorem ⋮ Risk excess measures induced by hemi-metrics ⋮ Four Areas of Yu. V. Prokhorov's Studies and Their Perspectives ⋮ On asymptotic proximity of distributions ⋮ Minimax estimators of parameters of a regression model ⋮ Convergence Rate of Random Geometric Sum Distributions to the Laplace Law ⋮ On the rate of convergence in a limit theorem for random symmetric polynomials ⋮ Esseen-Rozovskii type estimates for the rate of convergence in the Lindeberg theorem ⋮ A generalization of the Rozovskii inequality ⋮ A generalization of the Wang-Ahmad inequality ⋮ Functional limit theorems for sums of independent random variables with random coefficients ⋮ Convex and star-shaped sets associated with multivariate stable distributions. I: Moments and densities ⋮ Estimation of the convergence rate in a transfer theorem for centered random sums ⋮ Asymptotic behavior of compound nonordinary Cox processes with nonzero means ⋮ Probability metrics with applications in finance ⋮ A Moment Inequality with Application to Convergence Rate Estimates in the Global CLT for Poisson-Binomial Random Sums ⋮ One-dimensional empirical measures, order statistics, and Kantorovich transport distances ⋮ Estimates for the stability of decompositions of three-point distributions ⋮ On natural convergence rate estimates in the Lindeberg theorem ⋮ Relaxation, dispersion, attenuation, and finite propagation speed in viscoelastic media ⋮ Transport inequalities on Euclidean spaces for non-Euclidean metrics ⋮ Extended Poisson equation for weakly ergodic Markov processes ⋮ Stability of the characterization of normal distribution in the Laha-Lukacs theorem. ⋮ On exact order of convergence of random polynomials ⋮ B. V. Gnedenko: classic of limit theorems in the theory of probability ⋮ On the rates of convergence to symmetric stable laws for distributions of normalized geometric random sums ⋮ An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums

This page was built for publication: Modern Theory of Summation of Random Variables