Discretely uniform approximation of continuous functions

Discretely Observed Diffusions: Approximation of the Continuous-time Score Function

Discretely Observed Diffusions: Approximation of the Continuous-time Score Function

We discuss parameter estimation for discretely observed, ergodic diffusion processes where the diffusion coefficient does not depend on the parameter. We propose using an approximation of the continuous-time score function as an estimating function. The estimating function can be expressed in simple terms through the drift and the diffusion coefficient and is thus easy to calculate. Simulation ...

Uniform approximation of continuous functions on compact sets by biharmonic functions

We give a characterization of functions that are uniformly approximable on a compact subset K of R by biharmonic functions in neighborhoods of K.

The best uniform polynomial approximation of two classes of rational functions

In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.

UNIFORM APPROXIMATION BY b – HARMONIC FUNCTIONS

The Mergelyan and Ahlfors-Beurling estimates for the Cauchy transform give quantitative information on uniform approximation by rational functions with poles off K. We will present an analogous result for an integral transform on the unit sphere in C2 introduced by Henkin, and show how it can be used to study approximation by functions that are locally harmonic with respect to the Kohn Laplacia...