The motivation of this work is the study of the error term et (x,ω) in the averaging method for differential equations perturbed by a dynamical system. Results of convergence in distribution for ( e t (x,·) √ ε )ε>0 have been established in Khas’minskii [Theory Probab. Appl. 11 (1966) 211–228], Kifer [Ergodic Theory Dynamical Systems 15 (1995) 1143– 1172] and Pène [ESAIM Probab. Statist. 6 (200...

Using the main ideas of Tanaka, the measure-solution {Pt}t of a 3-dimensional spatially homogeneous Boltzmann equation of Maxwellian molecules without cutoff is related to a Poisson-driven stochastic differential equation. Using this tool, the convergence to {Pt}t of solutions {P l t}t of approximating Boltzmann equations with cutoff is proved. Then, a result of Graham-Méléard is used and allow...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

The well-known and very simple MinOver algorithm is reformulated for incremental support vector classification with and without kernels. A modified proof for itsO(t−1/2) convergence is presented, with t as the number of training steps. Based on this modified proof it is shown that even a convergence of at leastO(t−1) is given. This new convergence bound for MinOver is confirmed by computer expe...

We investigate the asymptotic properties as t → ∞ of the differential equation ẍ(t) + a(t)ẋ(t) +∇G(x(t)) = 0, t ≥ 0 where x(·) is R-valued, the map a : R+ → R+ is non increasing, and G : R → R is a potential with locally Lipschitz continuous derivative. We identify conditions on the function a(·) that guarantee or exclude the convergence of solutions of this problem to points in argminG, in the...

7 Acknowledgments We want to thank specially Stefan Mießbach for numerous contributions in proving the convergence properties of the net dynamic and for advice concerning the " cornered rat " example. We are very grateful to Ingrid Gabler for supplying the experimental data for this same example. 6.3 Convergence of the dynamic We show now the local convergence of the dynamic defined by the MF e...

7 Acknowledgments We want to thank specially Stefan Mießbach for numerous contributions in proving the convergence properties of the net dynamic and for advice concerning the " cornered rat " example. We are very grateful to Ingrid Gabler for supplying the experimental data for this same example. 6.3 Convergence of the dynamic We show now the local convergence of the dynamic defined by the MF e...

This paper presents a theoretical analysis of t h e s ta t ic and dynamic convergence behavior for a general class of adaptive blind equalizers. W e first s tudy t h e properties of prediction e r ro r functions of blind equalization algorithms, and t h e n we use these properties t o analyze t h e s ta t ic and dynamic convergence behavior based on t h e independence assumption. We prove in th...