Related papers: Complete moment convergence of moving average proc…

In this paper, the complete moment convergence for the partial sums of moving average processes $\{X_n=\sum_{i=-\infty}^{\infty}a_iY_{i+n},n\ge 1\}$ is proved under some proper conditions, where $\{Y_i,-\infty<i<\infty\}$ is a doubly…

Let $\{Y_i,-\infty<i<\infty\}$ be a doubly infinite sequence of identically distributed, negatively dependent random variables under sub-linear expectations, $\{a_i,-\infty<i<\infty\}$ be an absolutely summable sequence of real numbers. In…

For a sequence of identically distributed negatively associated random variables $\{X_n; n\geq 1\}$ with partial sums $S_n=\sum_{i=1}^nX_i, n\geq 1$, refinements are presented of the classical Baum-Katz and Lai complete convergence…

In this paper, we prove the equivalent conditions of complete moment convergence of the maximum for partial weighted sums of independent, identically distributed random variables under sublinear expectations space. As applications, the…

The complete convergence for weighted sums of sequences of independent, identically distributed random variables under sublinear expectations space was studied. By moment inequality and truncation methods, we establish the equivalent…

We investigate the complete $p$-th moment convergence for weighted sums of independent, identically distributed random variables under sublinear expectations space. Using moment inequality and truncation methods, we prove the equivalent…

We consider a new method of the semiparametric statistical estimation for the continuous-time moving average L\'evy processes. We derive the convergence rates of the proposed estimators, and show that these rates are optimal in the minimax…

We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…

For an array $\left\{X_{n,j}, \, 1 \leqslant j \leqslant k_{n}, n \geqslant 1 \right\}$ of random variables and a sequence $\{c_{n} \}$ of positive numbers, sufficient conditions are given under which, for all $\varepsilon > 0$,…

The paper is concerned with a class of two-sided stochastic processes of the form $X=W+A$. Here $W$ is a two-sided Brownian motion with random initial data at time zero and $A\equiv A(W)$ is a function of $W$. Elements of the related…

We study critera for a pair $ (\{ X_n \} $, $ \{ Y_n \}) $ of approximating processes which guarantee closeness of moments by generalizing known results for the special case that $ Y_n = Y $ for all $n$ and $ X_n $ converges to $Y$ in…

Let $\{X_n;n\ge 1\}$ be a sequence of independent random variables on a probability space $(\Omega, \mathcal{F}, P)$ and $S_n=\sum_{k=1}^n X_k$. It is well-known that the almost sure convergence, the convergence in probability and the…

Braverman, Mallows and Shepp (1995), showed that if the absolute moments of partial sums of i.i.d. symmetric variables are equal to those of normal variables, then the marginals have normal distribution. This fact suggested the conjecture…

We prove that the $k$-th positive integer moment of partial sums of Steinhaus random multiplicative functions over the interval $(x, x+H]$ matches the corresponding Gaussian moment, as long as $H\ll x/(\log x)^{2k^2+2+o(1)}$ and $H$ tends…

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…

In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval $(0,1)$. The proposed model accommodates a set of…

We consider the convergence of moving averages in the general setting of ergodic theory or stationary ergodic processes. We characterize when there is universal convergence of moving averages based on complete convergence to zero of the…

Let $(X,\mathcal{B},m,\tau)$ be a dynamical system with $\ds (X,\mathcal{B},m)$ a probability space and $\ds \tau$ an invertible, measure preserving transformation. The present paper deals with the almost everywhere convergence in…

Consider a sequence X_k=\sum_{j=0}^{\infty}c_j\xi_{k-j}, k\geq 1, where c_j, j\geq 0, is a sequence of constants and \xi_j, -\infty <j<\infty, is a sequence of independent identically distributed (i.i.d.) random variables (r.v.s) belonging…

Let $\{X, X_n, n\geq 1\}$ be a sequence of independent identically distributed non-degenerate random variables. Put $S_0=0, S_n = \sum^n_{i=1} X_i$ and $V_n^2=\sum^n_{i=1} X_i^2, n\ge 1.$ A weak convergence theorem is established for the…