We study the convergence rate of an asymptotic expansion for the elliptic and parabolic operators with rapidly oscillating coefficients. First we propose homogenized expansions which are convolution forms of Green function and given force term of elliptic equation. Then, using local Lp-theory, the growth rate of the perturbation of Green function is found. From the representation of elliptic so...

This paper develops a simple technique for proving the weak convergence of a stochastic process Z̄n(g) := ∫ g dZn, indexed by functions g in some class G. The main novelty is a decoupling argument that allows to derive asymptotic equicontinuity of the process {Z̄n(g), g ∈ G} from that of the basic process {Zn(t), t ∈ R}, with Zn(t) = Z̄n(ft) and ft(x) = 1(−∞,t](x). The method leads to novel result...

165 In this paper, we wish to analyze the convergence behavior of a number of neuronal plasticity models. Recent neurophysiological research suggests that the neuronal behavior is adaptive. In particular, memory stored within a neuron is associated with the synaptic weights which are varied or adjusted to achieve learning. A number of adaptive neuronal models have been proposed in the literatur...

We prove necessary and sufficient conditions for the almost sure convergence of the integrals ∫∞ 1 g(a(t)+Mt)df(t), ∫ 1 0 g(a(t)+Mt)df(t), and thus of ∫∞ 0 g(a(t)+Mt)df(t), where Mt = sup{|Xs| : s ≤ t} is the two-sided maximum process corresponding to a Lévy process (Xt)t≥0, a(·) is a nondecreasing function on [0,∞) with a(0) = 0, g(·) is a positive nonincreasing function on (0,∞), possibly wit...

Let E be a real uniformly convex Banach space which has the Fréchet differentiable norm, and K a nonempty, closed, and convex subset of E. Let T : K ® K be an asymptotically -strictly pseudocontractive mapping with a nonempty fixed point set. We prove that (I T) is demiclosed at 0 and obtain a weak convergence theorem of the modified Mann’s algorithm for T under suitable control conditions. Mor...

We study Γ-convergence for a sequence of parabolic function-als, F ε (u) = T 0 Ω f (x ε , t, ∇u)dxdt as ε → 0, where the integrand f is nonconvex, and periodic on the first variable. We obtain the representation formula of the Γ-limit. Our results in this paper support a conclusion which relates Γ-convergence of parabolic functionals to the associated gradient flows and confirms one of De Giorg...

Keywords: Filter Modular space (Modular) filter convergence Rate of convergence Sampling operator Integral operator Urysohn operator Mellin convolution operator a b s t r a c t We investigate the order of approximation of a real-valued function f by means of suitable families of sampling type operators, which include both discrete and integral ones. We give a unified approach, by means of which...

Part I [13] introduces the application of the barycentric approximation methodology for evaluating pro t-and-loss distributions numerically. Although, convergence of the quantiles is ensured by the weak convergence of the discrete measures, as proclaimed in [13], recent numerical results have indicated that the approximations of the pro t-and-loss distribution are less practical when the portfo...

We consider the standard problem of learning a concept from random examples. Here a learning curve can be deened to be the expected error of a learner's hypotheses as a function of training sample size. Haussler, Littlestone and Warmuth have shown that, in the distribution free setting, the smallest expected error a learner can achieve in the worst case over a concept class C converges rational...

Keywords: Fuzzy variable Independence Operation t-norm Convergence Law of large numbers a b s t r a c t T-independence of fuzzy variables is a more general concept than the classical independence. The objective of this study is to deal with some new properties of T-independent fuzzy variables. First of all, for any general t-norm, some criteria of T-independence are discussed for fuzzy variable...