Preface; Contents; 1 White Noise Analysis and Chaos Expansions; 1.1 Introduction; 1.2 Deterministic Background; 1.3 Spaces of Random Variables; 1.3.1 Gaussian White Noise Space; 1.3.2 Wiener-Itô Chaos Expansion of Random Variables; 1.3.3 Kondratiev Spaces; 1.3.4 Hilbert Space Valued Kondratiev Type Random Variables; 1.3.5 Wick Product; 1.3.6 Fractional Gaussian White Noise Space; 1.4 Stochastic Processes; 1.4.1 Chaos Expansion Representation of Stochastic Processes; 1.4.2 Schwartz Spaces Valued Stochastic Processes; 1.4.3 Fractional Operator mathcalM

1.4.4 Multiplication of Stochastic Processes1.5 Operators; References; 2 Generalized Operators of Malliavin Calculus; 2.1 Introduction; 2.2 The Malliavin derivative ; 2.3 The Skorokhod Integral; 2.4 The Ornstein-Uhlenbeck Operator; 2.5 Properties of the Operators of Malliavin Calculus; 2.6 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 Operator3.5 Wick-Type Equations Involving the Malliavin Derivative; 3.6 Integral Equation; References; 4 Applications and Numerical Approximation; 4.1 Introduction; 4.2 A Stochastic Optimal Control Problem in Infinite Dimensions; 4.2.1 State Equation with a Delta-Noise; 4.2.2 Random Coefficients; 4.2.3 Further Extensions; 4.3 Operator Differential Algebraic Equations; 4.3.1 Extension to Nonlinear Equations; 4.4 Stationary Equations; 4.5 A Fractional Optimal Control Problem; 4.6 Numerical Approximation; 4.6.1 Elliptic Equation