Some Blackwell-Type Renewal Theorems for Weighted Renewal Functions

Some Blackwell-type Renewal Theorems for Weighted Renewal Functions

In this paper, a new approach is proposed to investigate Blackwell-type renewal theorems for weighted renewal functions systematically according to which of the tails of weighted renewal constants or the underlying distribution is asymptotically heavier. Some classical results are improved considerably.

On Some General Renewal Theorems for Nonidentically Distributed Variables @bullet @bullet on Some General Renewal Theorems for Nonidentically Distributed Variables

in probability and statistics at Chapel Hill. Reproduction in whole or in part· is permitted for any purpose of the United States Government.

Renewal Theorems for Markov Chains

Limit Theorems for Renewal Processes

This article describes the Key renewal theorem and the Blackwell’s renewaltheorem. These two limit theorems for renewal processes are equivalent but of different forms.They are particularly useful for characterizing the asymptotic behavior of a probabilisticquantity of interest in a renewal process. We present two applications of these limit theorems:the limiting distributions o...

Bounds and Comparisons for Weighted Renewal-Type Integral Equations

In this note, inequalities and bounds for weighted renewal-type integral equations are presented. Some upper and lower bounds for the weighted renewal-type integral equations with monotone weight functions are derived. Some upper and lower bounds for the weighted renewal-type equations with monotone weight functions are derived. Bounds for the difference between two weighted renewal functions a...