相关论文: On the strong law of large numbers for L-statistic…
In this paper, under some weaker conditions, we give three laws of large numbers under sublinear expectations (capacities), which extend Peng's law of large numbers under sublinear expectations in [8] and Chen's strong law of large numbers…
In this work we derive a variant of the classic Glivenko-Cantelli Theorem, which asserts uniform convergence of the empirical Cumulative Distribution Function (CDF) to the CDF of the underlying distribution. Our variant allows for tighter…
The paper presents fundamental metrical theorems for a class of continued fraction-like expansions known as $\theta$-expansions. We first prove Khinchine's Weak Law of Large Numbers for the sum of digits, followed by the Diamond-Vaaler…
We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called deviation means of independent and identically distributed random variables (for the strong law of…
We extend the celebrated Glivenko-Cantelli theorem, sometimes called the fundamental theorem of statistics, from its standard setting of total variation distance to all $f$-divergences. A key obstacle in this endeavor is to define…
This paper presents the strong law of large numbers for a function of the local times of a transient random walk on groups, extending the research of Asymont and Korshunov for random walks on the integer lattice $\mathbb{Z}^d$. Under some…
This note proves a law of large numbers for predicting several steps ahead, which, in the case of uniformly bounded random variables, generalizes the standard law of large numbers for martingales; the standard law of large numbers…
Weak convergence of maxima of dependent sequences of identically distributed continuous random variables is studied under normalizing sequences arising as subsequences of the normalizing sequences from an associated iid sequence. This…
The validity of the strong law of large numbers for multiple sums $S_n$ of independent identically distributed random variables $Z_k$, $k\leq n$, with $r$-dimensional indices is equivalent to the integrability of $|Z|(\log^+|Z|)^{r-1}$,…
We establish weak and strong law of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the branching mechanism being general and…
As a kind of independence of random variables under sublinear expectations, pseudo-independence is weaker than Peng's independence. We shall give Marcinkiewicz-type weak and strong laws of large numbers for pseudo-independent random…
The objective of this paper is to investigate the layered structure of topological complexity in the tail of a probability distribution. We establish the functional strong law of large numbers for Betti numbers, a basic quantifier of…
A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 1. We deduce this behavior as a simple consequence of the statistical…
This paper explores various distributional aspects of random variables defined as the ratio of two independent positive random variables where one variable has an $\alpha$-stable law, for $0<\alpha<1$, and the other variable has the law…
As a part of our works on effective properties of probability distributions, we deal with the corresponding characteristic functions. A sequence of probability distributions is computable if and only if the corresponding sequence of…
This article provides a strong law of large numbers for integration on digital nets randomized by a nested uniform scramble. The motivating problem is optimization over some variables of an integral over others, arising in Bayesian…
In this paper, we investigate the functional central limit theorem and the Marcinkiewicz strong law of large numbers for U-statistics having absolutely regular data and taking value in a separable Hilbert space. The novelty of our approach…
In this paper we prove that, under certain conditions, a strong law of large numbers holds for a class of super-diffusions $X$ corresponding to the evolution equation $\partial_t u_t=L u_t+\beta u_t-\psi(u_t)$ on a bounded domain $D$ in…
Consider a supercritical superdiffusion (X_t) on a domain D subset R^d with branching mechanism -\beta(x) z+\alpha(x) z^2 + int_{(0,infty)} (e^{-yz}-1+yz) Pi(x,dy). The skeleton decomposition provides a pathwise description of the process…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.