算子逼近的概率论方法

Some Probabilistic Methods of Approximation

本文用概率论方法对在区间I∈R上只具有第一类间断点的函数f(x),用Feller算子给出了点态逼近。Feller算子包含许多常用的逼近算子,从而拓广了现有的结果。

Suppose that f(x) is a bounded function on I R with discontinuity of the first kind. Feller's operaters Ln(f,x) are defined as (1). In this paper we give the order of pointwise approximation of f by its Feller operators using some probabilistic methods.