An extremal problem arising in soil erosion modeling
An individual ergodic theorem for random fuzzy sets.
An integral representation for the Hellinger distance.
An invariance principle for the law of the iterated logarithm for some Markov chains
Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.
Analytically normed spaces.
Another look at the moment method for large dimensional random matrices.
Approximation at first and second order of -order integrals of the fractional Brownian motion and of certain semimartingales.
Asymptotic analysis for bifurcating autoregressive processes via a martingale approach.
Asymptotic direction for random walks in random environments
Asymptotic distributions and Berry-Esseen bounds for sums of record values.
Asymptotic properties and optimization of some non-Markovian stochastic processes
We study the limit behavior of certain classes of dependent random sequences (processes) which do not possess the Markov property. Assuming these processes depend on a control parameter we show that the optimization of the control can be reduced to a problem of nonlinear optimization. Under certain hypotheses we establish the stability of such optimization problems.
Asymptotic results for empirical measures of weighted sums of independent random variables.
Asymptotics for open-loop window flow control.
Asymptotics for the moment convergence of -statistics in LIL.
Autoregressive type martingale fields.
Barycentre canonique pour un espace métrique à courbure négative
Bernstein inequality for the parameter of the pth order autoregressive process AR(p)
The autoregressive process takes an important part in predicting problems leading to decision making. In practice, we use the least squares method to estimate the parameter θ̃ of the first-order autoregressive process taking values in a real separable Banach space B (ARB(1)), if it satisfies the following relation: . In this paper we study the convergence in distribution of the linear operator for ||θ̃|| > 1 and so we construct inequalities of Bernstein type for this operator.
Berry–Esseen theorem and local limit theorem for non uniformly expanding maps
Best possible sufficient conditions for strong law of large numbers for multi-indexed orthogonal random elements.
Block distribution in random strings
For almost all infinite binary sequences of Bernoulli trials the frequency of blocks of length in the first terms tends asymptotically to the probability of the blocks, if increases like (for ) where tends to . This generalizes a result due to P. Flajolet, P. Kirschenhofer and R.F. Tichy concerning the case .