Tijana Levajkovic, Hermann Mena

Equations Involving Malliavin Calculus Operators (eBook, PDF)

Applications and Numerical Approximation

• Format: PDF

Produktbeschreibung

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

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 132
• Erscheinungstermin: 31. August 2017
• Englisch
• ISBN-13: 9783319656786
• Artikelnr.: 53064463

Autorenporträt

Tijana Levajkovic 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.

Inhaltsangabe

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.

Rezensionen

"This book aims to give a unified introduction to stochasatic differential equations involving Malliavin calculus operators. The intended audience is that of researchers and graduate students interested in stochastic partial differential equations and related fields." (John Masson Noble, Mathematical Reviews, June, 2018)
"The intended audience are researchers and graduate students interested in stochastic partial differential equations and related fields. This book is self-contained for readers familiar with white noise analysis and Malliavin calculus." (Yuliya S. Mishura, zbMATH 1388.60007, 2018)