We consider Lipschitz and H\"{o}lder continuous random dynamical systems defined by a distribution with a finite logarithmic moment. We prove that under suitable non-degeneracy conditions every stationary measure must be $\log$-H\"{o}lder continuous.
Hölder regularity of stationary measures
The Decomposition Formula and Stationary Measures for Stochastic Lotka-Volterra Systems with Applications to Turbulent Convection
Decrease of Fourier coefficients of stationary measures
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