General Probability Theory
Eric Chin, Dian Nel, Sverrir Ólafsson · 2014
Probability theory is a branch of mathematics that deals with mathematical models of trials whose outcomes depend on chance. This chapter reviews some basic concepts of the probability theory that are needed to begin solving stochastic calculus problems. The set of all possible outcomes of an experiment is called the sample space. Any subset of the sample space is known as an event. The collection of events can be defined as a subcollection. The chapter focuses on an approach to probability which is a branch of measure theory. The reason for taking a measure-theoretic path is that it leads to a unified treatment of both discrete and continuous random variables, as well as a general definition of conditional expectation. The conditional expectation is extremely important in probability theory and also for its wide application in mathematical finance such as pricing options and other derivative products.