The Stochastic Dirichlet Problem Driven by the Ornstein–Uhlenbeck Operator: Approach by the Fredholm Alternative for Chaos Expansions

DOI10.1080/07362994.2011.548998zbMath1225.60107OpenAlexW1968902728MaRDI QIDQ3168707

Tijana Levajković, Dora Seleši, Stevan Pilipović

Publication date: 19 April 2011

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362994.2011.548998

zbMATH Keywords

Dirichlet problemWick productFredholm alternativeOrnstein-Uhlenbeck operatorMalliavin derivativeWiener-Ito chaos expansion

Mathematics Subject Classification ID

Generalized stochastic processes (60G20) White noise theory (60H40) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Applications of functional analysis in probability theory and statistics (46N30)

Related Items (6)

The stochastic linear quadratic optimal control problem in Hilbert spaces: a polynomial chaos approach ⋮ The Stochastic LQR Optimal Control with Fractional Brownian Motion ⋮ Operator differential-algebraic equations with noise arising in fluid dynamics ⋮ Nonhomogeneous First-order Linear Malliavin Type Differential Equation ⋮ Fundamental equations with higher order Malliavin operators ⋮ Malliavin calculus for generalized and test stochastic processes

Cites Work

• On the generalized stochastic Dirichlet problem. I: The stochastic weak maximum principle
• Weighted stochastic Sobolev spaces and bilinear SPDEs driven by space-time white noise
• The Malliavin Calculus and Related Topics
• EXPANSION THEOREMS FOR GENERALIZED RANDOM PROCESSES, WICK PRODUCTS AND APPLICATIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS
• NO ZERO DIVISOR FOR WICK PRODUCT IN (S)*
• Algebra of Generalized Stochastic Processes and the Stochastic Dirichlet Problem
• Stochastic Partial Differential Equations Driven by Purely Spatial Noise
• Elliptic equations of higher stochastic order
• Stochastic Differential Equations: A Wiener Chaos Approach
• On the generalized stochastic Dirichlet problem. II: Solvability, stability and the Colombeau case

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