While Chapter 10 is devoted to the notion of independence related to sums of random variables, this chapter is concerned with the concept of conditioning with respect to a -algebra. This plays an important role in key areas such as Markov processes, semimartingale theory and ergodic theory. Among others, Section 29 includes topics such as regular conditional probability, conditional independence and Markov triple. Applying results of this section, Section 30 contains a basic account of the theory of semimartingales in discrete time.
29 Conditional Expectations, Conditional Probabilities and Conditional Independence
In Section ...