相关论文: Three series theorem for independent random variab…
Linear combinations of independent random variables have been extensively studied in the literature. However, most of the work is based on some specific distribution assumptions. In this paper, a companion of (J. Appl. Probab. 48 (2011)…
We establish the Strassen's law of the iterated logarithm for independent and identically distributed random variables with $\hat{\mathbb{E}}[X_1]=\hat{\mathcal{E}}[X_1]=0$ and $C_{\mathbb{V}}[X_1^2]<\infty$ under sub-linear expectation…
We revisit the question of whether the strong law of large numbers (SLLN) holds uniformly in a rich family of distributions, culminating in a distribution-uniform generalization of the Marcinkiewicz-Zygmund SLLN. These results can be viewed…
The Marcinkiewicz--Zygmund theorem is a fundamental result in probability theory that establishes rates of convergence in the strong law of large numbers (SLLN). Although numerous extensions have been developed for dependent sequences, many…
In this paper, the improvement about the generalized Kolmogorov-type three series theorem, in the case of NQD random variables, is obtained by different method. Furthermore, the generalized Kolmogorov-type three series theorem is…
We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to the study of dependent random variables sampled by a $\bbZ$-valued transient random walk. This extends the results…
We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient…
By the well-known I.Kotlarski lemma, if $\xi_1$, $\xi_2$, and $\xi_3$ are independent real-valued random variables with nonvanishing characteristic functions, $L_1=\xi_1-\xi_3$ and $L_2=\xi_2-\xi_3$, then the distribution of the random…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
Algorithmic theories of randomness can be related to theories of probabilistic sequence prediction through the notion of a predictor, defined as a function which supplies lower bounds on initial-segment probabilities of infinite sequences.…
We study the free central limit theorem for not necessarily identically distributed free random variables where the limiting distribution is the semicircle distribution. Starting from an estimate for the Kolmogorov distance between the…
The classical problem of maximizing the Shannon entropy of a sum of independent random variables supported on a finite alphabet is considered and settled in the ternary case. Namely, the following theorem is established: if…
We consider a notion of uniform thinning for a finite sequence of random variables $(X_1,...,X_n)$ obtained by removing one random variable, uniformly at random. If a triangular array of random variables $(X_{n,k} : n \in \mathbb{N}_+, 1…
We utilize an ergodic theory framework to explore sublinear expectation theory. Specifically, we investigate the pointwise Birkhoff's ergodic theorem for invariant sublinear expectation systems. By further assuming that these sublinear…
The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. Even though this problem is extremely important in applications, its systematic study has begun recently. In this paper we…
Based on deleting-item central limit theory, the classical Donsker's theorem of partial-sum process of independent and identically distributed (i.i.d.) random variables is extended to incomplete partial-sum process. The incomplete…
Limit theorems for a random number of independent random variables are frequently called transfer theorems. Investigations into this direction for sums of random variables with independent random sample size have been originated by…
We propose and study a new model for competitions, specifically sports multi-player leagues where the initial strengths of the teams are independent i.i.d. random variables that evolve during different days of the league according to…