Stochastic Retarded Evolution Equations: Green Operators, Convolutions, and Solutions

DOI10.1080/07362990802007236zbMath1181.34086OpenAlexW2076041216MaRDI QIDQ3506305

Kai Liu

Publication date: 12 June 2008

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

Full work available at URL: https://doi.org/10.1080/07362990802007236

zbMATH Keywords

weak solutionfundamental solutionstrong solutionmild solutionstochastic convolutionBurkholder-Davis-Gundy type inequalitystochastic retarded differential equation

Mathematics Subject Classification ID

Functional-differential equations in abstract spaces (34K30) Stochastic functional-differential equations (34K50) Stochastic integral equations (60H20)

Related Items (11)

A Large Deviation Principle of Retarded Ornstein-Uhlenbeck Processes Driven by Lévy Noise ⋮ Approximate controllability for a semilinear stochastic evolution system with infinite delay in \(L_p\) space ⋮ On regularity property of retarded Ornstein-Uhlenbeck processes in Hilbert spaces ⋮ Vector-valued stochastic delay equations -- a semigroup approach ⋮ Vector-valued stochastic delay equations -- a weak solution and its Markovian representation ⋮ Stationary solutions of retarded Ornstein-Uhlenbeck processes in Hilbert spaces ⋮ Retarded stationary Ornstein-Uhlenbeck processes driven by Lévy noise and operator self-decomposability ⋮ 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 ⋮ A Criterion for Stationary Solutions of Retarded Linear Equations with Additive Noise ⋮ Infinitely delayed stochastic evolution equations on UMD Banach spaces

Cites Work

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• Optimal control of linear retarded systems in Banach spaces
• Theory and applications of partial functional differential equations
• An estimate of Burkholder type for stochastic processes defined by the stochastic integral
• A stopped Doob inequality for stochastic convolution integrals and stochastic evolution equations
• Some inequalities for martingales and stochastic convolutions
• On Semigroups in Rⁿ X L^p Corresponding to Differential Equations with Delays
• Stability of Infinite Dimensional Stochastic Differential Equations with Applications

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