Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions

DOI10.1016/j.na.2015.05.019zbMath1322.60122arXiv1407.6563OpenAlexW2963492772MaRDI QIDQ495239

Rong-Chan Zhu, Michael Roeckner, Xiang Chan Zhu

Publication date: 9 September 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.6563

zbMATH Keywords

martingale problemlocal monotonicitystochastic delay PDEstochastic functional-differential equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) PDEs in connection with fluid mechanics (35Q35) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic functional-differential equations (34K50) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

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Cites Work

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• Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise
• Stochastic Lagrangian particle approach to fractal Navier-Stokes equations
• SPDE in Hilbert space with locally monotone coefficients
• Attractors for 2D-Navier-Stokes models with delays
• Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations
• Existence and asymptotic behavior for hereditary stochastic evolution equations
• Lower bounds for an integral involving fractional Laplacians and the generalized Navier-Stokes equations in Besov spaces
• Martingale solutions and Markov selections for stochastic partial differential equations
• Classical Dirichlet forms on topological vector spaces - the construction of the associated diffusion process
• Existence, uniqueness, and asymptotic behavior of mild solutions to stochastic functional differential equations in Hilbert spaces
• Theory and applications of partial functional differential equations
• Stochastic functional evolution equations with monotone nonlinearity: existence and stability of the mild solutions
• A note on stochastic semilinear equations and their associated Fokker-Planck equations
• Sub and supercritical stochastic quasi-geostrophic equation
• A concise course on stochastic partial differential equations
• The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities
• Stochastic functional partial differential equations: existence, uniqueness and asymptotic decay property
• Asymptotic Behavior of a Class of Nonlinear Stochastic Heat Equations with Memory Effects
• Existence and uniqueness of solutions of stochastic functional differential equations
• Brownian Representations of Cylindrical Local Martingales, Martingale Problem and Strong Markov Property of Weak Solutions of SPDEs in Banach Spaces
• EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR DELAY STOCHASTIC EVOLUTION EQUATIONS
• Stochastic Equations in Infinite Dimensions

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