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The classic differential evolution algorithm and its convergence properties

Roman Knobloch, Jaroslav Mlýnek, Radek Srb (2017)

Applications of Mathematics

Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the...

The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces

Nguyen Van Huan, Nguyen Van Quang (2012)

Kybernetika

We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.

The dyadic fractional diffusion kernel as a central limit

Hugo Aimar, Ivana Gómez, Federico Morana (2019)

Czechoslovak Mathematical Journal

We obtain the fundamental solution kernel of dyadic diffusions in + as a central limit of dyadic mollification of iterations of stable Markov kernels. The main tool is provided by the substitution of classical Fourier analysis by Haar wavelet analysis.

The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in 𝕃 p

Jérôme Dedecker, Florence Merlevède (2007)

ESAIM: Probability and Statistics

Considering the centered empirical distribution function Fn-F as a variable in 𝕃 p ( μ ) , we derive non asymptotic upper bounds for the deviation of the 𝕃 p ( μ ) -norms of Fn-F as well as central limit theorems for the empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.

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