The narrow recurrence of random dynamical systems by Ahmed Zaou, Mohamed Amouch

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Regular Attractor by Strict Lyapunov Function for Random Dynamical Systems by Hind Adnan Hashim

“… The main objective of this paper is to study some types of random attractors in random dynamical systems based on the random strict Lyapunov   function. …”
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Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise by Caibin Zeng, Qigui Yang, Junfei Cao

“…Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation.…”
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Simple Rules of a Discrete Stochastic Process Leading to Catalan-like Recurrences by Mariusz Białecki

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(L2,H1)-Random Attractors for Stochastic Reaction-Diffusion Equation on Unbounded Domains by Gang Wang, Yanbin Tang

“…We study the random dynamical system generated by a stochastic reaction-diffusion equation with additive noise on the whole space ℝn and prove the existence of an (L2,H1)-random attractor for such a random dynamical system. …”
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Asymptotic Behavior of Stochastic Partly Dissipative Lattice Systems in Weighted Spaces by Xiaoying Han

“…We first show that these stochastic partly dissipative lattice differential equations generate a random dynamical system. We then establish the existence of a tempered random bounded absorbing set and a global compact random attractor for the associated random dynamical system.…”
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Random Attractors of Stochastic Three-Component Reversible Gray-Scott System on Unbounded Domains by Anhui Gu

“…The Gray-Scott system is recast as a random dynamical system and asymptotic compactness which is illustrated by using uniform, a priori estimates for far-field values of solutions and a cutoff technique.…”
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Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space by Yijin Zhang, Zongbing Lin

“…We first show the existence of a continuous random dynamical system for the equations. Then we investigate the pullback asymptotical compactness of solutions as well as the existence and uniqueness of tempered random attractor in Xρ space. …”
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Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains by Qiuying Lu, Guifeng Deng, Weipeng Zhang

“…We show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. We demonstrate that the system possesses a unique D-random attractor, for which the asymptotic compactness is established by the method of uniform estimates on the tails of its solutions.…”
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Random Attractors for Stochastic Retarded Reaction-Diffusion Equations on Unbounded Domains by Xiaoquan Ding, Jifa Jiang

“…We first show that the stochastic retarded reaction-diffusion equation generates a random dynamical system by transforming this stochastic equation into a random one through a tempered stationary random homeomorphism. …”
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Asymptotic behavior of non-autonomous stochastic Boussinesq lattice system by Ailing Ban

“…Then, we consider the existence of a uniform absorbing random set for a jointly continuous non-autonomous random dynamical system (NRDS) generated by the system, and make an estimate on the tail of solutions. …”
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Dynamics of a continued fraction of Ramanujan with random coefficients by Jonathan M. Borwein, D. Russell Luke

“…A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of random dynamical systems. We determine the convergence properties of stochastic difference equations and so the divergence of their corresponding continued fractions.…”
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