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Large deviation local limit theorems and limits of biconditioned planar maps
The Annals of Applied Probability, 2021We first establish new local limit estimates for the probability that a nondecreasing integer-valued random walk lies at time $n$ at an arbitrary value, encompassing in particular large deviation regimes.
I. Kortchemski, Cyril Marzouk
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Berry–Esseen Bounds with Targets and Local Limit Theorems for Products of Random Matrices
Journal of Geometric Analysis, 2021Let $$\mu $$ μ be a probability measure on $$\textrm{GL}_d(\mathbb {R})$$ GL d ( R ) and denote by $$S_n:= g_n \cdots g_1$$ S n : = g n ⋯ g 1 the associated random matrix product, where $$g_j$$ g j ’s are i.i.d.’s with law $$\mu $$ μ .
T. Dinh, Lucas Kaufmann, Hao-Yun Wu
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Expansions in the Local and the Central Limit Theorems for Dynamical Systems
Communications in Mathematical Physics, 2020We study higher order expansions both in the Berry–Esséen estimate (Edgeworth expansions) and in the local limit theorems for Birkhoff sums of chaotic probability preserving dynamical systems.
Kasun Fernando, Franccoise Pene
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Local Limit Theorems for Compound Discrete Distributions
Theory of Probability & Its Applications, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1975
We consider a sequence of independent random variables {X n ; n = 1, 2,…). We shall suppose for simplicity that these variables have a common distribution with zero mean and nonzero variance σ2 < ∞. If \({S_n} = \sum\limits_{j = 1}^n {{X_j}}\) and \({F_n}\left( x \right) = P\left( {{S_n} < x\sigma \sqrt n } \right)\), the assumptions imply that F n (x)
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We consider a sequence of independent random variables {X n ; n = 1, 2,…). We shall suppose for simplicity that these variables have a common distribution with zero mean and nonzero variance σ2 < ∞. If \({S_n} = \sum\limits_{j = 1}^n {{X_j}}\) and \({F_n}\left( x \right) = P\left( {{S_n} < x\sigma \sqrt n } \right)\), the assumptions imply that F n (x)
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Limit theorems for local polynomial estimation of regression for functional dependent data
AIMS MathematicsLocal polynomial fitting exhibits numerous compelling statistical properties, particularly within the intricate realm of multivariate analysis. However, as functional data analysis gains prominence as a dynamic and pertinent field in data science, the ...
Oussama Bouanani, Salim Bouzebda
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Central Limit Theorems of Local Polynomial Threshold Estimator for Diffusion Processes with Jumps
, 2017Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the non‐parametric local polynomial threshold estimator, especially local linear case, is employed to estimate the diffusion ...
Yuping Song, Hanchao Wang
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Local Limit Theorems for Stable Limit Distributions
Theory of Probability & Its Applications, 1962Let (1) be a sequence of independent integer valued random variables. One says that for sequence (1) the local limit theorem is true in strong form if for each sequence which differs from (1) in only a finite number of terms relation (3) is fulfilled. We prove the following theorem: Condition (4) is necessary and sufficient that for the sequence (1) of
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APERIODICITY OF COCYCLES AND CONDITIONAL LOCAL LIMIT THEOREMS
Stochastics and Dynamics, 2004We establish conditions for aperiodicity of cocycles (in the sense of [12]), obtaining, via a study of perturbations of transfer operators, conditional local limit theorems and exactness of skew-products. Our results apply to a large class of Markov and non-Markov interval maps, including beta transformations.
Zweimüller, Roland +3 more
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A LOCAL LIMIT THEOREM FOR CONTINUED FRACTIONS
Stochastics and Dynamics, 2010It is shown that functionals of digits in continued fraction expansion satisfy either the DeMoivre–Gnedenko or the Shepp–Stone limit theorems if and only if their marginals are in the domain of attraction of the normal law.
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