Yeh J. Martingales and stochastic analysis

World Scientific, 1995. — 512 p.This book is a thorough and self-contained treatise of martingales as a tool in stochastic analysis, stochastic integrals and stochastic differential equations. The book is clearly written and details of proofs are worked out.Stochastic Processes:
Generated σ-Algebras
Stochastic Processes
Stopping Times
Convergence in Lp and Uniform Integrability
Martingales:
Martingale, Submartingale and Supermartingale
Fundamental Submartingale Inequalities
Convergence of Submartingales
Uniformly Integrable Submartingales
Regularity of Sample Functions of Submartingales
Increasing Processes
Stochastic Integrals:
L2-Martingales and Quadratic Variation Processes
Stochastic Integrals with Respect to Martingales
Adapted Brownian Motions
Extensions of the Stochastic Integral
Itô's Formula
Itô's Stochastic Calculus
Stochastic Differential Equations:
The Space of Continuous Functions
Definition and Function Space Representation of Solution
Existence and Uniqueness of Solutions
Strong Solutions