The current paper is devoted to stochastic Ginzburg–Landau–Newell equation with degenerate stochastic forcing. First, we establish a type of gradient inequality, which is also essential to proving asymptotic strong Feller… Click to show full abstract
The current paper is devoted to stochastic Ginzburg–Landau–Newell equation with degenerate stochastic forcing. First, we establish a type of gradient inequality, which is also essential to proving asymptotic strong Feller property. Then, we prove that the corresponding dynamical system possesses a strong type of Lyapunov structure and is of a relatively weak form of irreducibility. Finally, we prove that the corresponding Markov semigroup possesses a unique, exponentially mixing invariant measure.
Journal Title: Stochastics and Dynamics
Year Published: 2019
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