The Brownian fractional motion as a limit of some types of stochastic processes.
The bundle convergence in von Neumann algebras and their -spaces
A stronger version of almost uniform convergence in von Neumann algebras is introduced. This "bundle convergence" is additive and the limit is unique. Some extensions of classical limit theorems are obtained.
The central limit problem for strictly stationary sequences [Abstract of thesis]
The central limit theorem for dynamical systems
The central limit theorem for Markov chains with the simultatneous total variation convergence of the chain.
The central limit theorem for random fields
The central limit theorem for stochastic integrals.
The classic differential evolution algorithm and its convergence properties
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 convergence of sums of transition probabilities of a positive recurrent Markov chain.
The distribution of divisors of N!
The distribution of unbounded random sets and the multivalued strong law of large numbers in nonreflexive Banach spaces.
The domain of attraction of a non-Gaussian stable distribution in a Hilbert space
The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces
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
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 dynamics of mutation-selection algorithms with large population sizes
The effect of random scale changes on limits of infinitesimal systems.
The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in
Considering the centered empirical distribution function Fn-F as a variable in , we derive non asymptotic upper bounds for the deviation of the -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.
The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
The ergodic theory of positive operators on continuous functions
The exit path of a Markov chain with rare transitions