Low-rate renewal theory and estimation

TL;DR

This paper extends renewal theorems to low-rate and high-drift scenarios, providing theoretical foundations for decentralized parameter estimation under severe communication constraints.

Contribution

It introduces new renewal theorems applicable when renewal rates approach zero or drift approaches infinity, with applications to decentralized estimation.

Findings

Extended renewal theorems for low-rate processes

Application to decentralized parameter estimation

Theoretical insights into renewal behavior under extreme conditions

Abstract

Certain renewal theorems are extended to the case that the rate of the renewal process goes to 0 and, more generally, to the case that the drift of the random walk goes to infinity. These extensions are motivated by and applied to the problem of decentralized parameter estimation under severe communication constraints.