Equations Involving Malliavin Calculus Operators: Applications and Numerical Approximation

1 White Noise Analysis and Chaos Expansions: 1.1   Introduction.- 1.3  Deterministic background.- 1.2   Spaces of random variables.- 1.4 Stochastic processes.- 1.5 Operators.- References.- 2 Generalized Operators of Malliavin Calculus: 2.1 Introduction.- 2.1  The Malliavin derivative.- 2.2   The Skorokhod integral.- 2.3   The Ornstein-Uhlenbeck operator.- 2.4 Properties of the Malliavin operators.- 2.5 Fractional operators of the Malliavin calculus.- References.- 3 Equations involving Mallivin Calculus Operators: 3.1  Introduction.- 3.2 Equations with the Ornstein-Uhlenbeck operator.- 3.3  First order equation with the Malliavin derivative operator.- 3.4  Nonhomogeneous equation with the Malliavin derivative operator.- 3.5 Wick-type equations involving the Malliavin derivative.- 3.6 Integral equation.- References.- 4 Applications and Numerical Approximation: 4.1 Introduction.- 4.1  A stochastic optimal control problem.- 4.3 Operator differential algebraic equations.- 4.4 Stationary equations.- 4.5 A fractional optimal control problem.- 4.6 Numerical approximation.- References.