scientific article; zbMATH DE number 3248575
From MaRDI portal
Publication:5535438
zbMath0154.42201MaRDI QIDQ5535438
Yu. V. Linnik, I. A. Ibragimov
Publication date: 1965
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Related Items
Selection of sampling numerical parameters for the DSMC method ⋮ On normal approximation of discounted and strongly mixing random variables ⋮ M-Mixing systems. I ⋮ Theoretical and numerical analysis of approaches to evaluation of statistical error of the DSMC method ⋮ Numerically statistical simulation of the intensity field of the radiation transmitted through a random medium ⋮ On moderate deviations for martingales ⋮ Uniform CLT for Markov chains and its invariance principle: A martingale approach ⋮ Estimates for the accuracy of coupling in the central limit theorem ⋮ On conditions for convergence of the densities of smoothed distributions in the central limit theorem ⋮ Semiexponential distributions and related large deviation principles for trajectories of random walks ⋮ On the model of random walk with multiple memory structure ⋮ The central limit theorem for \(\rho\)-mixing series patterns ⋮ On the probabilities of moderate deviations for combinatorial sums ⋮ Estimate of convergence rate in local limit theorem for the particle number in spin systems ⋮ Deviations of Fejer sums and rates of convergence in the von Neumann ergodic theorem ⋮ Mallows permutations and finite dependence ⋮ Stabilization of statistical solutions for an infinite inhomogeneous chain of harmonic oscillators ⋮ Large deviations of semimartingales via convergence of the predictable characteristics ⋮ Limit theorems for the maximal tree size of a Galton-Watson forest in the critical case ⋮ Asymptotic theory of density estimation ⋮ Asymptotic expansion for the distribution density function of the compound Poisson process in large deviations ⋮ Uniform convergence on subspaces in the von Neumann ergodic theorem with discrete time ⋮ On the dynamics of stationary shift processes with Cantor structure ⋮ Transport equation for the harmonic crystal coupled to a Klein-Gordon field ⋮ Formation of a relation of nonlocalities in the anomalous diffusion model ⋮ Competition between Lévy jumps and continuous drift ⋮ FINITELY DEPENDENT COLORING ⋮ On the uniform metric in the context of convergence to normality ⋮ Efficiency of a certain modification of the studentized range of symmetric stable random variables ⋮ Bernstein inequality under averaging of elliptic systems in periodic random media ⋮ Theorems on convergence of stochastic integrals distributions to signed measures and local limit theorems for large deviations ⋮ Some approaches to financial risk assessment ⋮ Averaging stochastic systems under weakly dependent perturbations ⋮ On Cramer approximations under violation of Cramer's condition ⋮ A lower bound of \(L_p\) norms in the CLT for strongly mixing random variables ⋮ New correlative randomized algorithms for statistical modelling of radiation transfer in stochastic medium ⋮ Finitely dependent cycle coloring ⋮ Domain of attraction of a stable law for the group of motions of Euclidean space ⋮ Fejér sums for periodic measures and the von Neumann ergodic theorem ⋮ Domain of attraction of a stable law for the group of motions of Euclidean space ⋮ Regularly Varying Sequences ⋮ Limit theorems for a random walk in a random environment ⋮ Non-uniform bounds in local limit theorems in case of fractional moments. II ⋮ Asymptotic properties of empirical estimates for parameters of Markov sequences ⋮ Asymptotic properties of estimates for unknown parameters of almost periodic functions under Gaussian noise ⋮ Normal approximation for linear stochastic processes and random fields in Hilbert space ⋮ Probabilities of large deviations for L-statistics ⋮ On the history of St. Petersburg school of probability and mathematical statistics. II: Random processes and dependent variables ⋮ Limit theorems for tapered Toeplitz quadratic functionals of continuous-time Gaussian stationary processes ⋮ Theory of dynamical systems and general transformation groups with invariant measure ⋮ Moment inequality for sums of multi-indexed dependent random variables ⋮ Asymptotic behavior of the remainder term in the central limit theorem ⋮ Estimate of the convergence rate in the central limit theorem for weakly dependent random variables ⋮ A multidimensional central limit theorem for sums of functions of sequences with mixing ⋮ Cumulants of polylinear forms of a stationary sequence ⋮ Multichannel service processes with intensive input flow. II ⋮ Some bounds for the distribution of sums of weakly independent random variables ⋮ Refinement of the rate of convergence of densities to the stable law with characteristic exponent \(0<\alpha<1\) in the \(L_p\) metric. ⋮ Local limit theorems for the probability of large deviations for the maximum of sums of independent random variables ⋮ Nonuniform estimate of the rate of convergence in the CLT with stable limit distribution ⋮ Determination of the average value of a stable process with independent increments ⋮ One form of estimating the rate of convergence to a normal law ⋮ Estimates for the moment-generating function for stationary random processes ⋮ Averaging of symmetric diffusion in random medium ⋮ Random walks with internal degrees of freedom ⋮ Asymptotics of the number of forests consisting of unrooted trees ⋮ Large-deviation theorems for sums of random variables connected in a Markov chain. I ⋮ Diffusion approximation of normalized integrals of weakly dependent processes and its applications ⋮ Distribution of certain functionals of spacings in a scheme of series ⋮ A criterion of vanishing of the spectral density based on homoclinic sums ⋮ Unnamed Item ⋮ On probabilities of moderate deviations of sums for independent random variables ⋮ Random broken lines that weakly converge to a fractional Ornstein-Uhlenbeck process ⋮ The principle of invariance in the Donsker form to the partial sum processes of finite order moving averages ⋮ Limit theorems for a nonreturning random walk in a Markov chain ⋮ Bounds of mixed semi-invariants of random processes ⋮ An analogue of the Baum-Katz theorem for weakly dependent random variables ⋮ On the largest component of the random graph at a nearcritical stage ⋮ On the normal approximation of a negative binomial random sum ⋮ Probability inequalities for sums of weakly dependent random variables ⋮ A combined approach to the estimation of statistical error of the direct simulation Monte Carlo method ⋮ Limit theorems for summation schemes on a stationary sequence in a scheme of series ⋮ Limit theorems for quadratic forms of linear processes ⋮ Regularized nonparametric filtering of signal with unknown distribution in nonlinear observation model ⋮ On the normal approximation under some condition for a differential equation of the characteristic function ⋮ Recurrence of random walks in the Ising spins ⋮ Operator algebras in statistical mechanics and noncommutative probability theory ⋮ Approximation of distributions of sums of Banach-valued random elements with infinitely divisible laws. I. ⋮ Estimate of the rate of convergence in the central limit theorem for weakly dependent random fields ⋮ Effective averaging of stochastic radiative models based on Monte Carlo simulation ⋮ Approximations of distributions of sums of lattice random variables. II ⋮ Central limit theorem for weakly dependent variables ⋮ Approximation of distributions of sums of weakly dependent random variables by the normal distribution ⋮ Limit behavior of sums of a random number of independent random variables ⋮ Accuracy of approximation of sums of independent random variables by a stable distribution ⋮ Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem ⋮ Local limit theorems for functionals in the conditional invariance principle ⋮ On the constants in the estimates of the rate of convergence in von Neumann's ergodic theorem ⋮ On the singular spectrum of powers and products of random matrices ⋮ On probabilities of large deviations in Banach spaces ⋮ Convergence to stable laws in relative entropy ⋮ Limit theorems for Toeplitz quadratic functionals of continuous-time stationary processes ⋮ A general lemma on probabilities of large deviations ⋮ Estimates of linear regression coefficients on a homogeneous random field ⋮ Fisher information and convergence to stable laws ⋮ Berry-Esseen bounds in the entropic central limit theorem ⋮ Central limit theorem for almost-stationary sequences ⋮ Convergence rate in integral limit theorem with stable limit law ⋮ Averaging elliptic equations with random coefficients ⋮ A case when convergence in the mean is equivalent to convergence in the Levy metric ⋮ Invariance principle for certain classes of random fields ⋮ On the normal approximation of a binomial random sum ⋮ Estimation of spectral densities of stationary processes ⋮ Large deviations for estimates of spectrum of stationary series ⋮ Large deviations for sums of independent weighted random variables ⋮ An invariance principle for estimating the correlation function of a homogeneous random field ⋮ Global limit theorems ⋮ Asymptotic number of forests from unrooted trees ⋮ A general lemma for the density of a distribution taking into account large deviations ⋮ Divisible statistics ⋮ Strong convergence and local limit theorems for functionals of supremum type ⋮ Asymptotic behavior of partial sums of a series of probabilities of large deviations ⋮ A refinement of S. N. Bernshtejn's inequality ⋮ Estimate of the remainder term in the limit theorem for denominators of continued fractions ⋮ Theorems on large deviations for randomly indexed sum of weighted random variables ⋮ Asymptotic expansion in the case of a stable limit law. I ⋮ Estimation of the rate of approximation to stable laws in C(S) ⋮ Analysis of empirical estimates obtained for Gibbs distribution parameters by the maximum likelihood method ⋮ Analytic properties of quasistable distributions ⋮ Nonuniform estimate of rate of convergence to stable laws in certain Banach spaces ⋮ On convergence of kernel estimators of density with variable window width by dependent observations ⋮ Averaging in parabolic systems subject to weakly dependent random actions. The \(L_ 2\)-approach ⋮ Estimating the mixing rate for Markov processes ⋮ Cramér type large deviations for a class of statistics ⋮ Asymptotic properties of the sign estimate of autoregression field coefficients ⋮ Bayes type estimates ⋮ Asymptotic behavior of solutions of some classes of stochastic equations and their applications to statistical problems ⋮ Gibbsian random fields for lattice systems with pairwise interactions. ⋮ Some remarks on stable stochastic processes and \(\alpha\)-superharmonic functions ⋮ The Lévy-Khinchin representation of the one class of signed stable measures and some its applications ⋮ Local limit theorem in \(L_p\) for the case of convergence to normal law ⋮ On higher spectral densities of stationary processes with mixing ⋮ On the moments of a multidimensional distribution attracted to the stable distribution ⋮ Local limit theorems in \(L_p\) ⋮ On a local limit theorem for bounded random variables ⋮ Rate of convergence in the multidimensional limit theorem with a stable limit law ⋮ Convergence rate in the local mean limit theorem for a limiting stable law ⋮ Number of distinct sites visited by a random walk with internal states ⋮ Some global theorems for sums of independent random variables in which the existence of third-order moments is not assumed ⋮ Sharpening of the convergence rate in the multidimensional local limit theorem with stable limiting law ⋮ Refinement of speed of convergence to a stable law ⋮ On normal approximation for strongly mixing random variables ⋮ An asymptotic expansion in the case of a stable approximation law ⋮ Limit distributions of extreme order statistics of weakly dependent random variables ⋮ Convergence for densites in metric \(L_1\) for the limit stable law in the two-dimensional case ⋮ Local limit theorems for sums of i.i.d distributed random vectors. III ⋮ Nonuniform estimate of the rate of convergence to a stable law in the multidimensional central limit theorem ⋮ Domains of attraction of mixing sequences ⋮ Estimates of cumulants and centered moments of mixing stochastic processes ⋮ Limit theorems for sums of asymptotically independent random variables ⋮ Admissibility of the nonparametric analog of the Pitman estimate in the case of one unknown parameter ⋮ Smoothness of distribution function of \({\mathcal F}{\mathcal L}\)-statistic. I ⋮ Estimation of the autoregression parameter with infinite dispersion of noise ⋮ Rate of convergence in the central limit theorem for random variables with strong mixing ⋮ Finitely dependent processes are finitary ⋮ On the rate of convergence of \(L_p\) norms in the CLT for Poisson and gamma random variables ⋮ Limit theorems for sums of linearly generated random variables ⋮ Some bounds on closeness of distributions in terms of characteristic functions ⋮ Self-similar random fields ⋮ On the basic states of one-dimensional disordered structures ⋮ Convergence to stable laws and the modeling of them ⋮ Zones of attraction of self-similar multiple integrals ⋮ Asymptotic expansions for densities and distributions of weighted sums of independent random variables ⋮ A problem of A. N. Kolmogorov from the theory of the summation of independent random variables ⋮ Central limit theorem for functionals of a linear process ⋮ Asymptotic expansions for probability distributions. II ⋮ Fibering method in some probabilistic problems ⋮ Efficient estimation of the stationary distribution for exponentially ergodic Markov chains ⋮ Ideas in the theory of random media ⋮ Local structure of the spectrum of a one-dimensional random Schrödinger operator
