On the asymptotic uniform distribution of stochastic clearing processes

Abstract

Referring to a result of Sebfozo and Stidham [13] it is shown that under mild conditions, which can be easily verified

holds almost (c < 0) where x(u) = Y(u) mod c 0≦ X (u) ≦ c, and {Y(u)} is a real valued stochastic process with stationary increments and continuos non-decreasing trajectories

Keywords:

• Stochastic Clearing Process
• Inventory System
• Ergodic Theorem
• Asymptotic Uniform Distribution
• Random Measure
• Palm Distribution