DETERMINISTIC AND STOCHASTIC LINEAR TIME-SCALE SYSTEMS

Xiaolin Li (USA) and Jun Wang (USA)

Abstract

In this paper, we introduce the concept of deterministic and stochastic linear time-scale systems. We prove that under certain conditions, a large cascade of deterministic linear time-scale systems tends to a lognormal function, and a large cascade of stochastic linear time-scale systems tends to a lognormal process.

Keywords and phrases: deterministic linear time-scale system, stochastic linear time-scale system, integrable function, integrable process, lognormal function, lognormal process.