Martingales and stochastic analysis / J. Yeh

Information About

This monograph is an introduction to martingales and stochastic analysis assuming only real analysis and some basic concepts in probability theory. Stochastic independence, conditional expectation, and regular conditional probability are included in the appendix. of concision. Details of proofs are worked out for readability and for reference. Ghapter 1 begins with a collection of theorems concerning -algebras. Chapter 2 introduces martingale and submartingale properties as monotonicity conditions in terms of conditional expectation. Chapter 3 treats Ito's stochastic integral in the language of martingale theory. Chapter 4 starts with a study of the space of continuous functions on which solutions of stochastic differential equations will be constructed.