相关论文: On the functional limits for sums of a function of…

We obtain a functional central limit theorem (CLT) for sums of the form $\xi_N(t)=\frac1{\sqrt N}\sum_{n=1}^{[Nt]}\big(F(X(q_1(n)),...,X(q_\ell(n)))-\bar F\big)$ where $q_1,...,q_\ell$ are polynomials.

Let $(X_i,i\geq 1)$ be a sequence of i.i.d. random variables with values in $[0,1]$, and $f$ be a function such that $`E(f(X_1)^2)<+\infty$. We show a functional central limit theorem for the process $t\mapsto \sum_{i=1}^n f(X_i)1_{X_i\leq…

We derive a central limit theorem for sums of a function of independent sums of independent and identically distributed random variables. In particular we show that previously known result from Rempa\la and Weso\lowski (Statist. Probab.…

We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a Z d-random walk in different frameworks: probabilistic (when the r.f. is i.i.d. or a moving average of i.i.d. random…

In this paper we show a functional central limit theorem for the sum of the first $\lfloor t n \rfloor$ diagonal elements of $f(Z)$ as a function in $t$, for $Z$ a random real symmetric or complex Hermitian $n\times n$ matrix. The result…

In this paper we will prove a functional central limit theorems for "nonconventional" sums indexed by polynomial arrays.

In this paper, we investigate the functional central limit theorem for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation…

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

Using the regenerative scheme of Comets, Fern\'andez and Ferrari (2002), we establish a functional central limit theorem (FCLT) for discrete time stochastic processes (chains) with summable memory decay. Furthermore, under stronger…

Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…

Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a…

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The convergence takes place in the space of…

We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a 2d-random walk in different situations: when the r.f. is iid with a second order moment (random sceneries), or when it is…

In this paper we study the functional central limit theorem for stationary Markov chains with self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n; and…

It is shown that two conjectures put forward in the recent article Iksanov and Kostohryz (2025) are true. Namely, we prove a functional central limit theorem (FCLT) and a law of the iterated logarithm (LIL) for a random Dirichlet series…

In this work we study and establish some quenched functional Central Limit Theorems (CLTs) for stationary random fields under a projective criteria. These results are functional generalizations of the theorems obtained by Zhang et al.…

This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…

We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…

Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…