Conditional Semiamarts and Conditional Amarts

Abstract

In this note we give definition and basic properties of conditional amarts and conditional semiamarts. The aim of this note is to prove almost surely (a.s.) convergence theorem for conditional amarts. Moreover, in special cases we obtain a characterization of almost sure convergence in terms of weak convergence and the classical amart convergence theorem. The notion of conditional amarts unifies two ways of characterization of almost sure convergence.