Unification of Probability Theory on Time Scales

Abstract

The theory of time scales was introduced by Stefan Hilger in his PhD thesis in 1988 in order to unify continuous and discrete analysis. Probability is a discipline in which appears to be many applications of time scales. Time scales approach to probability theory unifies the standard discrete and continuous random variables. We give some basic random variables on the time scales. We define the distribution functions on time scales and show their properties.