We show the existence of solution for a strongly coupled elliptic system under three different conditions, namely: the autonomous case, the radial case, and a general case. For the autonomous case, we present a characterization of the solution.

The difference equations ξk = af(ξk−1) + εk, where (εk) is a square integrable difference martingale, and the differential equation dξ = −af(ξ)dt + dη, where η is a square integrable martingale, are considered. A family of estimators depending, besides the sample size n (or the observation period, if time is continuous) on some random Lipschitz functions is constructed. Asymptotic optimality of...

Using forward optimality criteria, we analyze a portfolio choice problem when the local risk tolerance is time-dependent and asymptotically linear in wealth. This class corresponds to a dynamic extension of the traditional (static) risk tolerances associated with the power, logarithmic and exponential utilities. We provide explicit solutions for the optimal investment strategies and wealth proc...

This article concerns the diffusion system ∂tu−∆xu + V (x)u = g(t, x, v), −∂tv −∆xv + V (x)v = f(t, x, u), where z = (u, v) : R × RN → R2, V (x) ∈ C(RN , R) is a general periodic function, g, f are periodic in t, x and asymptotically linear in u, v at infinity. We find a minimizing Cerami sequence of the energy functional outside the Nehari-Pankov manifold N and therefore obtain ground state so...

In this paper we will discuss a procedure to improve the usual estimator of a linear functional of the unknown regression function in inverse nonparametric regression models. In Klaassen et al. (2001) it has been proved that this traditional estimator is not asymptotically efficient (in the sense of the Hájek Le Cam convolution theorem) except, possibly, when the error distribution is normal. S...

We consider the problem of determing the existence of exponential dichotomy for a class of linear nonautonomous ODEs. An approach is introduced that combines numerical techniques with rigorous perturbation theory. It is applicable to a given problem within the class we consider and for practical purposes we develop a continuation technique. Numerical results illustrate the utility of the approach.

We study the area requirement of bar-visibility and rectangle-visibility representations of trees in the plane. We prove asymptotically tight lower and upper bounds on the area of such representations, and give linear-time algorithms that construct representations with asymptotically optimal area. @ 1997 Elsevier Science B.V.

The problem of estimating the marginal density of a linear process by kernel methods is considered. Under general conditions, kernel density estimators are shown to be asymptotically normal. Their limiting covariance matrix is computed. We also find the optimal bandwidth in the sense that it asymptotically minimizes the mean square error of the estimators. The assumptions involved are easily ve...

This note examines stability properties of systems that result from switching among globally asymptotically stable nonlinear systems in triangular form. We show by means of a counterexample that, unlike in the linear case, such a switched system might not be globally asymptotically stable, uniformly over all switching signals. We then formulate conditions that guarantee this uniform global asym...

In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space  with a uniformly G$hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(ell_{p})$ spaces, $1 < p