ABSTRACT
This chapter introduces random measure which are the most useful tools to investigate the jumps of semimartingales. By using jump measures, it establishes the integral representation of semimartingales, in connection with which the predictable characteristics of semimartingales are introduced. The chapter provides another simple but useful type of semimartingales — step processes, which play an important role in applied probability and statistics. It presents theorems and lemmas for semimartingale and Levy processes.
