Keywords: Bernstein operators Pointwise approximation Rate of convergence a b s t r a c t In the present paper, we study pointwise approximation by Bernstein–Durrmeyer type operators in the mobile interval x 2 0; 1 À 1 nþ1 h i , with use of Peetre's K-functional and x 2 u k ðf ; tÞ ð0 6 k 6 1Þ, we give its properties and obtain the direct and inverse theorems for these operators.

This paper makes three contributions to the literature on the nonparametric estimation of diffusion processes. First, we show that the nonparametric estimator of the drift function proposed by Stanton (J. of Finance, 1997) is not consistent. Second, we show that a proposed alternative nonparametric estimator of the drift function converges to the true drift in probability, in addition to provid...

R D = f(Ci, Ri, 1 ≤ i ≤ N), where f(·) is a possibly random real valued function, N ∈ {0, 1, 2, 3, . . . } ∪ {∞}, {Ci}i∈N are real valued random weights and {Ri}i∈N are iid copies of R, independent of (N,C1, C2, . . . ); D = represents equality in distribution. In the recent paper [10], an Implicit Renewal Theorem was developed that enables the characterization of the power tail asymptotics of ...

We provide an explanation of the main ideas underlying Götze's main result in [9] using Stein's method. We also provide detailed derivations of various intermediate estimates. Curiously, we are led to a different dimensional dependence of the constant than that given in [9]. We would like to dedicate this to Charles Stein on the occasion of his 90th birthday.

Lower-extremity movement in bipedal walking is characterized by a foot-rolling motion that includes heel-strike and toe-off. We investigated the dynamical influence of this movement on walking stability using a simple walking model that has a circular arc at the end of each leg. The leg is driven by a rhythmic signal from an internal oscillator to generate walking. We focused on stability chara...

The performance of individual agents in a group depends critically on the quality of information available to it about local and global goals and resources. In general it is assumed that the more accurate and up-to-date the available information, the better is the expected performance of the individual and the group. This conclusion can be challenged in a number of scenarios. We investigate the...

Suppose that X1, . . . , Xn, . . . , are independent, identically-distributed, rotationally invariant N×N matrices. Let Πn = Xn . . . X1. It is known that n −1 log ‖Πn‖ converges to a non-random limit. We prove that under certain additional assumptions on matrices Xi the speed of convergence to this limit does not decrease when the size of matrices, N, grows.

We consider a beam whose cross-section is a tubular neighborhood, with thickness scaling with a parameter δε, of a simple curve γ whose length scales with ε. To model a thin-walled beam we assume that δε goes to zero faster than ε, and we measure the rate of convergence by a slenderness parameter s which is the ratio between ε2 and δε. In this Part I of the work we focus on the case where the c...