On an algorithm for solving Fredholm integrals of the first kind

作     者：Chae, Minwoo Martin, Ryan Walker, Stephen G. 

作者机构：Case Western Reserve Univ Dept Math Appl Math & Stat Cleveland OH 44106 USA North Carolina State Univ Dept Stat Raleigh NC 27695 USA Univ Texas Austin Dept Math Austin TX 78712 USA 

出 版 物：《STATISTICS AND COMPUTING》 (统计学与计算)

年 卷 期：2019年第29卷第4期

页      面：645-654页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：NSF [DMS-1611791  DMS-1612891] 

主　　题：Brownian motion first passage time Convergence Expectation-maximization Iterative algorithm Mixture model 

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.