title: Dynamics of the stochastic Lorenz chaotic system with long memory effects.
abstract: Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.
authors.affiliation: School of Mathematics, South China University of Technology, Guangzhou 510640, People's Republic of China.
authors.forename: Caibin
authors.initials: C
authors.lastname: Zeng
authors.affiliation: School of Mathematics, South China University of Technology, Guangzhou 510640, People's Republic of China.
authors.forename: Qigui
authors.initials: Q
authors.lastname: Yang