ABSTRACT
This chapter introduces some fundamental facts about the weak convergence of distributions for stochastic processes. It discusses some deeper properties of convergent sequences under the Skorokhod topology. The chapter gives general results of weak convergence of measures on Polish space and the conditions of tightness for stochastic processes. It characterizes the weak convergence of step processes in terms of the weak convergence of jump times and jump sizes. The chapter presents theorems and lemmas for Skorokhod topology. Markov step processes and the approximation of Markov step processes via Markov sequences are also discussed.
