A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement
A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system
In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system are established....
A discrete approach to the chaotic representation property
A functional central limit theorem for martingales in C(K) and its application to sequential estimates.
A generalized Chacon's inequality and order convergence of processes
A limiting distribution for quicksort
A log-type moment result for perpetuities and its application to martingales in supercritical branching random walks.
A martingale central limit theorem
A maximal inequality of non-negative submartingale.
A multiplier theorem for Fourier series in several variables
We define a new type of multiplier operators on , where is the N-dimensional torus, and use tangent sequences from probability theory to prove that the operator norms of these multipliers are independent of the dimension N. Our construction is motivated by the conjugate function operator on , to which the theorem applies as a particular example.
A Non-Central Functional Limit Theorem for Quadratic Forms in Martingale Difference Sequences
A nonergodic version of Gordin's CLT for integrable stationary processes
A note on dilations and martingales.
A note on maximal inequalities
A note on martingale transforms and -weights
A note on the martingale central limit theorem
A note on the martingale inequality.
A Paley type inequality for two-parameter Vilenkin-Fourier coefficients.
A recurrence theorem for square-integrable martingales
Let be a zero-mean martingale with canonical filtration and stochastically -bounded increments which means that a.s. for all n ≥ 1, t > 0 and some square-integrable distribution H on [0,∞). Let . It is the main result of this paper that each such martingale is a.s. convergent on V < ∞ and recurrent on V = ∞, i.e. for some c > 0. This generalizes a recent result by Durrett, Kesten and Lawler [4] who consider the case of only finitely many square-integrable increment distributions....
A sharp analysis on the asymptotic behavior of the Durbin–Watson statistic for the first-order autoregressive process
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin–Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise....