A Criterion for Stationary Solutions of Retarded Linear Equations with Additive Noise

DOI10.1080/07362994.2011.598789zbMath1237.60051OpenAlexW1992881483MaRDI QIDQ3094222

Kai Liu

Publication date: 21 October 2011

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

Full work available at URL: https://doi.org/10.1080/07362994.2011.598789

zbMATH Keywords

stationary solutionGreen operatorretarded linear equation with additive noisestrong quasi-Feller property

Mathematics Subject Classification ID

Diffusion processes (60J60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (6)

On stationarity of stochastic retarded linear equations with unbounded drift operators ⋮ A Large Deviation Principle of Retarded Ornstein-Uhlenbeck Processes Driven by Lévy Noise ⋮ On regularity property of retarded Ornstein-Uhlenbeck processes in Hilbert spaces ⋮ Stability in distribution for stochastic differential equations with memory driven by positive semigroups and Lévy processes ⋮ Stationary distributions of second order stochastic evolution equations with memory in Hilbert spaces ⋮ Ergodicity and stationary solution for stochastic neutral retarded partial differential equations driven by fractional Brownian motion

Cites Work

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• Stability of functional partial differential equations
• Stationary solutions of retarded Ornstein-Uhlenbeck processes in Hilbert spaces
• Extending a theorem of A. M. Liapunov to Hilbert space
• Stochastic Retarded Evolution Equations: Green Operators, Convolutions, and Solutions
• Ergodicity for Infinite Dimensional Systems
• STATIONARY SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH MEMORY AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
• Mathematical control theory: an introduction

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