Moment generating function and generalized Feller operators
type: Item
instance of: scholarly article
zbMATH Open document ID: 0979.41013
author: Jihua Xu
author: Zeyin Zhang
publication date: 2002-02-21T00:00:00Z
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 1616540
zbMATH Keywords: generalized Feller
zbMATH Keywords: moment generating
zbMATH Keywords: unbounded function
zbMATH Keywords: approximation degree
MaRDI profile type: Publication
title: Moment generating function and generalized Feller operators
published in: Acta Mathematica Scientia. Series A. (Chinese Edition)
review text: Let \(\{X_i\}\) be the sequence of random variables with independent identical distribution (denoted by i.i.d.r.v sequence), \(EX_i=x\), \(x\in(-\infty, +\infty)\), we denote by \(S_n=X_1+ X_2+\cdots +X_n\), the distribution function of \(S_n\) be \(F_{n,x}(t)\), for \(j\in C_B(-\infty, +\infty)\) Feller operators are defined by NEWLINE\[NEWLINEF_n(f_ix): =Ef\left({S_n\over n}\right)= \int^\infty_{-\infty} f\left({t\over n} \right)dF_{n,x}(t),NEWLINE\]NEWLINE where \(E\) denotes mathematical expectation. If mathematical expectation \(EX_i\varphi(x)\), the authors generalize the Feller operators: let \(\{X_i\}\) be i.i.d.r.v sequence, \(EX_i= \varphi(x)\), \(\varphi(x\) be strictly increasing function on \([0,R)\) \((R\) is a finite positive number or \(+\infty)\), its inverse function \(\psi(x)\), \(\text{Var} X_i= \sigma^2(x)< +\infty\), generalized Feller operators are defined by NEWLINE\[NEWLINEL_n(f;x): =Ef\left[\psi \left({S_n\over n}\right) \right]= \int_0^{+ \infty} f\left[\psi \left({S_n\over n}\right)\right]d F_{n,x}(t),\;x\in [0,R),NEWLINE\]NEWLINE the special case of \(L_n(f;x)\) is the Meyer-König and Zeller operator. Applying the calculative property of moment generating functions and probabilistic methods, in the paper the convergence and estimation of approximation degree to unbounded functions for generalized Feller operators are obtained.
description: scientific article; zbMATH DE number 1616540