Table of Contents

INTRODUCTION TO ITO CALCULUS: Some Motivating Remarks; Some Fundamental Ideas: Previsible Processes, Localizabtion, etc; The Elementary Theory of Finite-Variation Processes; Stochastic Integrals: The L2 Theory; Stochastic Integrals with Respect to Continuous Semimartingales; Applications of Ito 's Formula; STOCHASTIC DIFFERENTIAL EQUATIONS AND DIFFUSIONS: Introduction; Pathwise Uniqueness, Strong SDEs, Flows; Weak Solutions, Uniqueness in Law; Martingale Problems, Markov Property; Overture to Stochastic Differential Geometry; One-Dimensional SDEs; One-Dimensional Diffusions; THE GENERAL THEORY: Orientation; The Debut and Section Theorems; Optional Projections and Filtering; Characterizing Previsible Times; Dual Previsible Projections; The Meyer Decomposition Theorem; Stochastic Integration: The General Case; Excursion Theory.