On the 2-orthogonal polynomials and the generalized birth and death processes.
On the abstract subordinated exit equation.
On the accuracy of approximation of the distribution of negative-binomial random sums by the gamma distribution
The main goal of this paper is to study the accuracy of approximation for the distributions of negative-binomial random sums of independent, identically distributed random variables by the gamma distribution.
On the adaptive control of countable Markov chains
On the adaptive wavelet estimation of a multidimensional regression function under -mixing dependence: Beyond the standard assumptions on the noise
We investigate the estimation of a multidimensional regression function from observations of an -mixing process , where , represents the design and the noise. We concentrate on wavelet methods. In most papers considering this problem, either the proposed wavelet estimator is not adaptive (i.e., it depends on the knowledge of the smoothness of in its construction) or it is supposed that is bounded or/and has a known distribution. In this paper, we go far beyond this classical framework....
On the almost sure convergence of weighted sums of random elements in D(0,1).
On the amount of information resulting from empirical and theoretical knowledge.
We present a mathematical model allowing formally define the concepts of empirical and theoretical knowledge. The model consists of a finite set P of predicates and a probability space (Ω, S, P) over a finite set Ω called ontology which consists of objects ω for which the predicates π ∈ P are either valid (π(ω) = 1) or not valid (π(ω) = 0). Since this is a first step in this area, our approach is as simple as possible, but still nontrivial, as it is demonstrated by examples. More realistic approach...
On the analogy between self-gravitating Brownian particles and bacterial populations
We develop the analogy between self-gravitating Brownian particles and bacterial populations. In the high friction limit, the self-gravitating Brownian gas is described by the Smoluchowski-Poisson system. These equations can develop a self-similar collapse leading to a finite time singularity. Coincidentally, the Smoluchowski-Poisson system corresponds to a simplified version of the Keller-Segel model of bacterial populations. In this biological context, it describes the chemotactic aggregation...
On the approach to equilibrium for a polymer with adsorption and repulsion.
On the approximate solutions of the Stratonovitch equation.
On the approximation of an integral by a sum of random variables.
On the approximation properties of Bernstein polynomials via probabilistic tools.
On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies
Let be the collection of all -optimal solutions for a stochastic process with locally bounded trajectories defined on a topological space. For sequences of such stochastic processes and of nonnegative random variables we give sufficient conditions for the (closed) random sets to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.
On the asymptotic behavior of the second moment of the Fourier transform of a random measure.
On the Asymptotic Behaviour of Convolution Powers of Probabilities on Discrete Groups.
On the asymptotic behaviour of increasing self-similar Markov processes.
On the Asymptotic Behaviour of Linear Learning Processes with Partial Forgetting.
On the asymptotic behaviour of sequences of random variables and of their previsible compensators
On the asymptotic behaviour of stationary gaussian processes
On the asymptotic equidistribution of sums of independent identically distributed random variables