Equations Involving Malliavin Calculus Operators

Friendly approach for solving stochastic equations with singular data
Novel applications of operators of the Malliavin calculus
From theoretical to numerical results of SPDEs with singular data

Friendly approach for solving stochastic equations with singular data Novel applications of operators of the Malliavin calculus From theoretical to numerical results of SPDEs with singular data Includes supplementary material: sn.pub/extras

Autorentext

Tijana Levajkovi is currently a postdoctoral researcher at the at the Department of Mathematics, University of Innsbruck. Her main research interests are in the fields of functional and stochastic analysis, particularly in infinite dimensional stochastic analysis, white noise analysis, Maliavin calculus, generalized stochastic processes, stochastic partial differential equations, algebras of generalized functions and optimal control.

Hermann Mena is professor at Yachay Tech, Ecuador. He also has an affiliation at the Department of Mathematics of Univeristy of Innsbruck, Austria. His research interests include applied mathematics, numerical analysis and optimal control. Particularly, deterministic and stochastic optimal control theory, numerical methods for optimal control problems and uncertainty quantification.

Zusammenfassung
Friendly approach for solving stochastic equations with singular data
Novel applications of operators of the Malliavin calculus
From theoretical to numerical results of SPDEs with singular data

Inhalt

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.