Probability
Abstract
This chapter is an introduction to probability and stochastic processes. The theory of Fourier transforms is used to discuss the concept of characteristic functions and their use in convergence theorems and in identifying measures. It includes the notion of submartingales and martingales presented first as an application of differentiation theory presented earlier. This is generalized to the situation of conditional expectation given a σ algebra and the relationship is discussed. Major theorems are the strong law of large numbers and the central limit theorem.
Fields of Study & Subjects
Probability and Statistical Research
Stochastic processes and statistical mechanics
Stochastic processes and financial applications
Publication details
- Journal / source
- Chapman & Hall/CRC eBooks
- Pages
- 349–388
- Publication date
- 10 January 2026
- Language
- EN
- Document type
- Book chapter