Renewal theory from the point of view of the theory of probability

摘要: Renewal theory is ordinarily reduced to the of certain types integral equations. Since basis for equations a simple probability process, however, it be expected that treatment in terms probability, which uses modern developments this theory, will shed new light on subject. The purpose paper present such treatment. simplest case, deals with following situation. A population individuals at hand; when any individual dies he immediately replaced by newly born individual. problem investigate development population, particularly age distribution. are supposed live and die independently each other sufficient most purposes consider consisting time only single At birth, future lifetime chance variable distribution function F(x) (the death before x). x, remaining then has