On an algorithm for solving Fredholm integrals of the first kind

被引：7

作者：

Chae, Minwoo ^{[1
]}

Martin, Ryan ^{[2
]}

Walker, Stephen G. ^{[3
]}

机构：

[1] Case Western Reserve Univ, Dept Math Appl Math & Stat, Cleveland, OH 44106 USA

[2] North Carolina State Univ, Dept Stat, Raleigh, NC 27695 USA

[3] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

STATISTICS AND COMPUTING | 2019年 / 29卷 / 04期

关键词：

Brownian motion first passage time; Convergence; Expectation-maximization; Iterative algorithm; Mixture model;

D O I：

10.1007/s11222-018-9829-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we use an iterative algorithm for solving Fredholm equations of the first kind. The basic algorithm and convergence properties are known under certain conditions, but we provide a simpler convergence proof without requiring the restrictive conditions that have previously been needed. Several examples of independent interest are given, including mixing density estimation and a first passage time density function involving Brownian motion. We also develop the basic algorithm to include functions which are not necessarily non-negative and, again, present illustrations.

引用

页码：645 / 654

页数：10

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