Manfred Denker

Manfred Denker
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Manfred Denker
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Mathematics - Dynamical Systems (5)
 
Mathematics - Probability (2)
 
Mathematics - Numerical Analysis (1)
 
Statistics - Methodology (1)

Publications Authored By Manfred Denker

We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler distributions, both in the weak topology of distributions and a.s. Read More

We prove a conditional local limit theorem for discrete-time fractional Brownian motions (dfBm) with Hurst parameter 3/4Read More

We relate the local specification and periodic shadowing properties. We also clarify the relation between local weak specification and local specification if the system is measure expansive. The notion of strong measure expansiveness is introduced, and an example of a non-expansive systems with the strong measure expansive property is given. Read More

A dynamical array consists of a family of functions $\{f_{n,i}: 1\le i\le k(n), n\ge 1\}$ and a family of initial times $\{\tau_{n,i}: 1\le i\le k(n), n\ge 1\}$. For a dynamical system $(X,T)$ we identify distributional limits for sums of the form $$ S_n= \frac 1{s_n}\sum_{i=1}^{k(n)} [f_{n,i}\circ T^{\tau_{n,i}}-a_{n,i}]\qquad n\ge 1$$ for suitable (non-random) constants $s_n>0$ and $a_{n,i}\in \mathbb R$, where the functions $f_{n,i}$ are locally Lipschitz continuous. Although our results hold for more general dynamics, we restrict to Gibbs-Markov dynamical systems for convenience. Read More

We prove an almost sure weak limit theorem for simple linear rank statistics for samples with continuous distributions functions. As a corollary the result extends to samples with ties, and the vector version of an a.s. Read More

We give a simple and elementary proof of the identity $$\sum_{r=1}^n\sum_{k_1,... Read More

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1Read More

We propose a new algorithm for generating pseudorandom (pseudo-generic) numbers of conformal measures of a continuous map T acting on a compact space X and for a Holder continuous potential F. In particular, we show that this algorithm provides good approximations to generic points for hyperbolic rational functions of degree two and the potential -h log|T'|, where h denotes the Hausdorff dimension of the Julia set of T . Read More