Results 1 to 10 of about 169,791 (145)
Central and Local Limit Theorems for Numbers of the Tribonacci Triangle [PDF]
Mathematics, 2021 In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of ...
Igoris Belovas
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Local limit theorems without assuming finite third moment [PDF]
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 +2 more
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Local limit theorems in free probability theory [PDF]
, 2010 In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands. We prove not only the uniform convergence of the densities to the semicircular density but also their $L^p ...
Jiun-Chau Wang
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Local Limit Theorem for Randomly Deforming Billiards [PDF]
Communications in Mathematical Physics, 2020 We study limit theorems in the context of random perturbations of dispersing billiards in finite and infinite measure. In the context of a planar periodic Lorentz gas with finite horizon, we consider random perturbations in the form of movements and deformations of scatterers.
Mark F. Demers +2 more
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Local limit theorems and mod-phi convergence [PDF]
Latin American Journal of Probability and Mathematical Statistics, 2019 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 ...
Borgo, Martina dal +2 more
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Local central limit theorems in stochastic geometry [PDF]
Electronic Journal of Probability, 2011 We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance.
Penrose, Mathew D., Peres, Yuval
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Local limit theorems via Landau-Kolmogorov inequalities
Bernoulli, 2015 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 ...
Ross, Nathan, Röllin, Adrian
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A Local Limit Theorem for Associated Sequences [PDF]
The Annals of Probability, 1985 A local central limit theorem of the type due to \textit{L. A. Shepp} [Ann. Math. Stat. 35, 419-423 (1964; Zbl 0146.391)] is proved for certain stationary sequences of associated random variables.
Thomas E. Wood
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Annealed and quenched limit theorems for random expanding dynamical systems [PDF]
Probability Theory and Related Fields, 2014 In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a central limit ...
Aimino, Romain +2 more
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Local limit theorems for ladder epochs [PDF]
, 2007 Let {S_n, n=0,1,2,...} be a random walk generated by a sequence of i.i.d. random variables X_1, X_2,... and let tau be the first descending ladder epoch. Assuming that the distribution of X_1 belongs to the domain of attraction of an alpha-stable law, we study the asymptotic behavior of P(tau=n).
Vladimir Vatutin, Vitali Wachtel
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