Square-mean pseudo almost automorphic process and its application to stochastic evolution equations

DOI10.1016/j.jfa.2011.03.005zbMath1233.60030OpenAlexW2000981578MaRDI QIDQ537712

Wei Lin, Zhang Chen

Publication date: 20 May 2011

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2011.03.005

zbMATH Keywords

global stabilitycompletenesscompositionevolution familysemigroup theorystochastic evolution equationssquare-mean pseudo-almost automorphic function

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions (43A60)

Related Items

Existence and global attractiveness of a square-mean μ-pseudo almost automorphic solution for some stochastic evolution equation driven by Lévy noise ⋮ Square-mean \(\mu \)-pseudo almost periodic and automophic solutions for a class of semilinear integro-differential stochastic evolution equations ⋮ Mean-square asymptotically almost automorphic solutions to fractional stochastic relaxation equations ⋮ LaSalle-type stationary oscillation principle for stochastic affine periodic systems ⋮ Almost automorphic solution for some stochastic evolution equation driven by Lévy noise with coefficients \(S^{2}\)-almost automorphic ⋮ Existence of almost automorphic mild solutions to non-autonomous neutral stochastic differential equations ⋮ Mean-square almost automorphic solutions for stochastic differential equations with hyperbolicity ⋮ Stepanov-like weighted asymptotic behavior of solutions to some stochastic differential equations in Hilbert spaces ⋮ Some periodic type solutions for stochastic reaction-diffusion equation with cubic nonlinearities ⋮ Compact almost automorphic solutions for semilinear parabolic evolution equations ⋮ Almost automorphic solutions to some stochastic functional differential equations with delay ⋮ Square-mean weighted pseudo almost automorphic solutions for non-autonomous stochastic evolution equations ⋮ Measure theory and square-mean pseudo almost periodic and automorphic process: application to stochastic evolution equations ⋮ Existence of periodic solutions in distribution for stochastic Newtonian systems ⋮ Almost automorphic solutions of dynamic equations on time scales ⋮ Time discretization and convergence to superdiffusion equations via Poisson distribution ⋮ On almost automorphic mild solutions for nonautonomous stochastic evolution equations ⋮ Unnamed Item ⋮ Wong-Zakai approximations and periodic solutions in distribution of dissipative stochastic differential equations ⋮ Almost automorphic random functions in probability ⋮ The solutions with recurrence property for stochastic linearly coupled complex cubic-quintic Ginzburg–Landau equations ⋮ Almost automorphic solutions of non-autonomous differential equations ⋮ Measure theory and \(S^2\)-pseudo almost periodic and automorphic process: application to stochastic evolution equations ⋮ Poisson \(S^2\)-almost automorphy for stochastic processes and its applications to SPDEs driven by Lévy noise ⋮ Asymptotic behavior of solutions to abstract stochastic fractional partial integrodifferential equations ⋮ Pseudo almost automorphic in distribution solutions of semilinear stochastic integro-differential equations by measure theory ⋮ Pseudo almost automorphic solution to stochastic differential equation driven by Lévy process ⋮ Quadratic-mean pseudo almost periodic solutions to some stochastic differential equations in a Hilbert space ⋮ Stepanov-like pseudo almost automorphic solutions to some stochastic differential equations ⋮ Square-mean pseudo almost automorphic mild solutions for stochastic evolution equations driven byG-Brownian motion ⋮ Existence and stability of \(\mu\)-pseudo almost automorphic solutions for stochastic evolution equations ⋮ Existence of pseudo almost automorphic mild solutions to stochastic fractional differential equations ⋮ Asymptotically almost automorphic solutions of dynamic equations on time scales ⋮ Weighted pseudo almost automorphic solutions for nonautonomous SPDEs driven by Lévy noise ⋮ Existence and exponential stability of almost pseudo automorphic solution for neutral stochastic evolution equations driven by G-Brownian motion ⋮ Pseudo almost automorphic mild solution of nonautonomous stochastic functional integro-differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument \([t + 1/2\)]
• On the almost automorphy of bounded solutions of differential equations with piecewise constant argument
• Weighted pseudo almost periodic functions and applications
• Global exponential stability of almost periodic solution for a large class of delayed dynamical systems
• Pseudo-almost periodicity of some nonautonomous evolution equations with delay
• Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces
• Pseudo almost periodic solutions to parabolic boundary value inverse problems
• Some properties of pseudo-almost automorphic functions and applications to abstract differential equations
• Existence and uniqueness of pseudo almost automorphic mild solutions to some classes of partial hyperbolic evolution equations
• Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications
• Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations
• Almost periodic differential equations
• Pseudo almost periodic solutions of some differential equations
• Pseudo-almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument
• Existence, uniqueness, and asymptotic behavior of mild solutions to stochastic functional differential equations in Hilbert spaces
• Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. I
• Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II
• Almost automorphic mild solutions to fractional differential equations
• Composition of pseudo almost automorphic and asymptotically almost automorphic functions
• Almost periodic linear differential equations with non-separated solutions
• Pseudo almost periodic solutions to some non-autonomous neutral functional differential equations with unbounded delay
• Almost automorphic and pseudo-almost automorphic mild solutions to an abstract differential equation in Banach spaces
• Square-mean almost automorphic solutions for some stochastic differential equations
• UNIFORM CONVERGENCE OF MONOTONE SEQUENCES OF FUNCTIONS
• Using white noise to enhance synchronization of coupled chaotic systems
• Complete and generalized synchronization in a class of noise perturbed chaotic systems
• Almost periodic solutions of affine stochastic evolution equations
• Periodic and almost periodic solutions for semilinear stochastic equations
• Stationary and almost periodic solutions of almost periodic affine stochastic differential equations
• Topics in Almost Automorphy
• Almost automorphic solutions of semilinear evolution equations
• Existence of almost periodic solutions to some stochastic differential equations
• Almost Automorphic Functions on Groups
• Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non dense domain
• Stochastic differential equations. An introduction with applications.