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On a Local Limit Theorem for Lattice Distributions
Theory of Probability & Its Applications, 1957Let sequence (1) of independent random variables assuming only integral values satisfy conditions (A) and (B). The following proposition is proved:In order for correlation (2) to hold true for a sequence differing from (1) only by a finite number of terms, it is necessary and sufficient for (3) to be satisfied.
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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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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.
Zweimueller, R +3 more
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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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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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Local Limit Theorems for Large Deviations
Theory of Probability & Its Applications, 1957Let $(X_j ),j = 1,2, \cdots $, be a sequence of independent random variables with the distribution functions $V_j (x)$. We assume the existence of ${\bf D}X_j = \sigma _j^2 ,s_n^2 = \sum\nolimits_{j = 1}^n {\sigma _j^2 } ,{\bf E}X_j = 0,j = 1,2, \cdots $. We put \[ Z_n = \sum\limits_{j = 1}^n X_j /s_n .
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A Local Limit Theorem for Moderate Deviations
Bulletin of the London Mathematical Society, 2001The author establishes a uniform estimate for the mass function \(P(S_m =y)\) of an integer-valued random walk when \(y\to\infty\) and \((y-m\mu)/ \sqrt{m} \to \infty,\) where \(\mu\) is the mean of the step distribution. The assumptions are that the mass function \(p\) of the step distribution is regularly varying at \(\infty\) with \(-\kappa\), where
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A Local Limit Theorem for Random Strict Partitions
Theory of Probability & Its Applications, 2000The authors consider a set of partitions of a natural number \(n\) on distinct summands with uniform distribution. They investigate the limit shape of the typical partition as \(n\to\infty\), which was found by \textit{A. M. Vershik} [Funct. Anal. Appl. 30, 90--105 (1996); translation from Funkts. Anal. Prilozh. 30, No. 2, 19--39 (1996; Zbl 0868.05004)]
Vershik, A. M. +2 more
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On the rate of conveergence in the local limit theorem for densities
Journal of Mathematical Sciences, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Korolev, V. Yu., Zhukov, Yu. V.
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Local Limit Theorems for Functionals of Random Processes
Theory of Probability & Its Applications, 1989The author proved the convergence in variation of functionals in random processes by using the method described in his earlier paper, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova, 142, 48-54 (1985; Zbl 0618.60038); English translation in J. Sov. Math. 36, 468-473 (1987).
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