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.
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页码：645 / 654
页数：10
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