A Sample-Path Condition for the Asymptotic Uniform Distribution of Clearing Processes

Abstract

In this note we show that the asymptotic time-average distribution of a functional of cumulative input process associated with an imbedded point process follows as asymptotic uniform distribution almost surely under a mild regulatory sample-path condition. Examples from stochastic clearing processes, inventory systems and renewal theory are provided.

Keywords:

• Asymptotic Uniform Distribution
• Stochastic Clearing Process
• Sample-path Analysis
• Inventory Systems
• Renewal Theory