Related papers: On the functional central limit theorem with mean-…
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…
Lacunary function systems of type $(f(M_nx))_{n\geq 1}$ for periodic functions $f$ and sequences of fast-growing matrices $(M_n)_{n\geq 1}$ exhibit many properties of independent random variables like satisfying the Central Limit Theorem or…
In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative…
We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal…
We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…
As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…
We prove a central limit theorem for a random field generated by d commuting probability preserving transformations; the martingale is given by a commuting filtration (cf. D. Khosnevisan, Multiparameter Processes, Springer 2002). The result…
Recently a new type of central limit theorem for belief functions was given in Epstein et al. [9]. In this paper, we generalize the central limit theorem in Epstein et al. [9] to accommodate general bounded random variables. These results…
We derive the continuous canonical distribution only by requiring the extensivity of the mean energy and the multiplicative probabilistic composition rule. The derivation is independent of the thermodynamic limit and moreover it does not…
We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of…
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
In this paper, we obtain a new estimate for uniform integrability under sublinear expectations. Based on this, we establish the limit theorems under nonlinear expectations dominated by sublinear expectations through tightness, and the limit…
This paper provides refined versions of some known functional central limit theorems for conditional Poisson sampling which are more suitable for applications. The theorems presented in this paper are generalizations of some results that…
The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical…
This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study…
We consider a non-nestling random walk in a product random environment. We assume an exponential moment for the step of the walk, uniformly in the environment. We prove an invariance principle (functional central limit theorem) under almost…
For nonnegative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows to construct new distributions with support (0,1), and to obtain a…
In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems…
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.