Results 211 to 220 of about 726,506 (255)

Local Limit Theorems for Stable Limit Distributions

Theory of Probability & Its Applications, 1962
Let (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
openaire   +1 more source

APERIODICITY OF COCYCLES AND CONDITIONAL LOCAL LIMIT THEOREMS

Stochastics and Dynamics, 2004
We 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, Aaronson, Jon, Denker, Manfred, Sarig, Omri   +3 more
openaire   +1 more source

A LOCAL LIMIT THEOREM FOR CONTINUED FRACTIONS

Stochastics and Dynamics, 2010
It 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.
openaire   +2 more sources

Local Limit Theorems for Lattice Random Variables

Theory of Probability & Its Applications, 1992
See the review Zbl 0748.60028.
openaire   +2 more sources

A Local Limit Theorem for Moderate Deviations

Bulletin of the London Mathematical Society, 2001
The 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
openaire   +1 more source

Relationship between Local and Integral Limit Theorems

Theory of Probability & Its Applications, 1996
Let \(\{S_n\}\) be the row-sums of a triangular array of row-independent random vectors. The sequence \(\{S_n\}\) obeys an integral limit theorem if \(\sup_{|x|= 1} |Q_n x|\to 0\) and \(Q_n(S_n - A_n)\) converges weakly to an absolutely continuous (AC) distribution with continuous density function \(g(x)\) for some real sequence \(\{A_n\}\) and ...
openaire   +2 more sources

Local Limit Theorem

2023
Zhen-Qing Chen, Takashi Kumagai, Laurent Saloff-Coste, Jian Wang, Tianyi Zheng   +4 more
openaire   +1 more source

Local Limit Theorems for Functionals of Random Processes

Theory of Probability & Its Applications, 1989
The 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).
openaire   +3 more sources

On local limit theorems. I

Lithuanian Mathematical Transactions, 1974
Mitalauskas, A., Statulevičius, V.
openaire   +3 more sources

Local limit theorems for free groups

Mathematische Annalen, 2001
Let \(G\) be the free group on \(k\geq 2\) generators. For \(g\in G\), let \(|g|\) be its word length and \([g]\in\mathbb{Z}^k\) its image under the Abelianization map \(G\to\mathbb{Z}^k\). Let \(W(n)=\{g\in G:|g|=n\}\) and, for fixed \(\alpha=(\alpha_1,\dots,\alpha_k)\in\mathbb{Z}^k\), let \(W(n,\alpha)=\{g\in W(n):[g]=\alpha\}\).
openaire   +1 more source