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Local limit theorems without assuming finite third moment

Journal of Inequalities and Applications, 2023
One of the most fundamental probabilities is the probability at a particular point. The local limit theorem is the well-known theorem that estimates this probability.
Punyapat Kammoo, Kittipong Laipaporn, Kritsana Neammanee   +2 more
doaj   +2 more sources

Classical and almost sure local limit theorems [PDF]

Dissertationes Mathematicae, 2022
We present and discuss the many results obtained concerning a famous limit theorem, the local limit theorem, which has many interfaces, with Number Theory notably, and for which, in spite of considerable efforts, the question concerning conditions of ...
Z. Szewczak, Michel J. G. Weber
semanticscholar   +3 more sources

Local limit theorems and mod-phi convergence [PDF]

Latin American Journal of Probability and Mathematical Statistics, 2017
We prove local limit theorems for mod-{\phi} convergent sequences of random variables, {\phi} being a stable distribution. In particular, we give two new proofs of a local limit theorem in the framework of mod-phi convergence: one proof based on the ...
M. D. Borgo, Pierre-Loic M'eliot, A. Nikeghbali   +2 more
semanticscholar   +4 more sources

Reassessing the Strength of a Class of Wigner’s Friend No-Go Theorems [PDF]

Entropy
Two recent, prominent theorems—the “no-go theorem for observer-independent facts” and the “Local Friendliness no-go theorem”—employ so-called extended Wigner’s friend scenarios to try to impose novel, non-trivial constraints on the possible nature of ...
Elias Okon
doaj   +2 more sources

Local limit theorems via Landau–Kolmogorov inequalities [PDF]

Bernoulli, 2010
In this article, we prove new inequalities between some common probability metrics. Using these inequalities, we obtain novel local limit theorems for the magnetization in the Curie-Weiss model at high temperature, the number of triangles and isolated ...
Adrian Röllin, Nathan Ross
semanticscholar   +4 more sources

Strong Large Deviation and Local Limit Theorems [PDF]

The Annals of Probability, 1993
Let \(\{Y_ n, n \geq 1\}\) be a sequence of random variables which converge weakly to a random variable \(Y\). The pseudodensity function of \(Y_ n\) is defined by \(q_ n(y;b_ n,S)= {b_ n \over \mu(S)}P(b_ n(Y_ n-y) \in S)\), where \(b_ n \to \infty\), \(\mu\) is the Lebesgue measure on \(R\) and \(S\) is a measurable subset of \(R\) such that ...
N. R. Chaganty, J. Sethuraman
semanticscholar   +4 more sources

Conditioned local limit theorems for random walks on the real line [PDF]

Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2021
Consider a random walk $S_n=\sum_{i=1}^n X_i$ with independent and identically distributed real-valued increments $X_i$ of zero mean and finite variance. Assume that $X_i$ is non-lattice and has a moment of order $2+\delta$.
Ion Grama, Hui Xiao
semanticscholar   +1 more source

Local Limit Theorems for Complex Functions on $\mathbb{Z}^d$ [PDF]

, 2022
The local (central) limit theorem precisely describes the behavior of iterated convolution powers of a probability distribution on the d-dimensional integer lattice, Z.
Evan Randles
semanticscholar   +1 more source

On the local limit theorems for lower psi-mixing Markov chains [PDF]

Latin American Journal of Probability and Mathematical Statistics, 2021
. In this paper we investigate the local limit theorem for additive functionals of nonstationary Markov chains that converge in distribution. We consider both the lattice and the non-lattice cases.
F. Merlevède, M. Peligrad, C. Peligrad
semanticscholar   +1 more source

The asymptotic of the density of the k-th maxima of independent random variables

Lietuvos Matematikos Rinkinys, 2023
In this paper the local limit theorem for density of k-th maxima of independent identically distributed random variables is proved.
Arvydas Jokimaitis
doaj   +3 more sources