On stability for a class of semilinear stochastic evolution equations

DOI10.1016/S0304-4149(97)00062-8zbMath0911.60049OpenAlexW2038377438MaRDI QIDQ1275962

Kai Liu

Publication date: 14 January 1999

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

Full work available at URL: https://doi.org/10.1016/s0304-4149(97)00062-8

zbMATH Keywords

mild solutionsalmost sure stabilitystochastic evolution equations

Mathematics Subject Classification ID

Stochastic stability in control theory (93E15) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (20)

Robustness of Pathwise Stability of Semilinear Perturbed Stochastic Evolution Equations ⋮ Stabilization of a class of semilinear degenerate parabolic equations by Itô noise ⋮ STABILITY OF STOCHASTIC DELAYED SIR MODEL ⋮ Global stability of a stochastic differential equation with discontinuous coefficients in a Hilbert space ⋮ Almost sure weak exponential stability with a certain decay function of semilinear stochastic evolution equations ⋮ Stabilization by multiplicative Itô noise for Chafee-Infante equation in perforated domains ⋮ Stabilization of Partial Differential Equations by Lévy Noise ⋮ On stabilization of partial differential equations by noise ⋮ Stability of non-densely defined semilinear stochastic evolution equations with application to the stochastic age-structured model ⋮ Stability analysis of semilinear stochastic differential equations ⋮ LARGE TIME DECAY BEHAVIOR OF DYNAMICAL EQUATIONS WITH RANDOM PERTURBATION FEATURES ⋮ P-th moment growth bounds of infinite-dimensional stochastic evolution equations ⋮ Moment decay rates of solutions of stochastic differential equations ⋮ Well-posedness of the Cauchy problem for stochastic evolution functional equations ⋮ Asymptotics of solutions to semilinear stochastic wave equations ⋮ Stability of solutions of stochastic functional-differential equations with locally Lipschitz coefficients in Hilbert spaces ⋮ Moment decay rates of infinite dimensional stochastic evolution equations with memory and Markovian jumps ⋮ Asymptotic behavior of the stochastic Kelvin–Voigt–Brinkman–Forchheimer equations ⋮ Long time behavior of stochastic McKean-Vlasov equations ⋮ Asymptotic exponential stability for diffusion processes driven by stochastic differential equations in duals of nuclear spaces

Cites Work

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• Stability of nonlinear stochastic-evolution equations
• Stability of semilinear stochastic evolution equations
• Semimartingales: A course on stochastic processes
• Existence and uniqueness for solutions of non-linear stochastic partial differential equations
• Asymptotic stability of the linear Ito equation in infinite dimensions
• Asymptotic exponential stability of stochastic partial differential equations with delay
• An estimate of Burkholder type for stochastic processes defined by the stochastic integral
• Stochastic partial differential equations with delays
• Stochastic Equations in Infinite Dimensions

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