3. Stochastic Calculus of Variations

Abstract

• 3.1 Introduction

  • 3.1.1 Notation

• 3.2 Flat Integral Representation of Wiener Measure

• 3.3 The Wiener Sphere

• 3.4 B-M on the Wiener Sphere and the Infinite Dimensional O-U Process

• 3.5 Malliavin operator

  • 3.5.1 Notation and preliminaries

  • 3.5.2 The Wiener-Itô chaos decomposition

  • 3.5.3 The derivation operator

  • 3.5.4 The Skorohod integral

  • 3.5.5 The Malliavin operator