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We prove the existence and uniqueness of invariant measures for thefractional stochastic Burgers equation (FSBE) driven by fractional power of theLaplacian and space-time white noise. We show also that the transition measuresof the solution converge to the invariant measure in the norm of totalvariation. To this end we show first two results which are of independentinterest: that the semigroup corresponding to the solution of the FSBE isstrong Feller and irreducible.

Ergodic properties of Fractional Stochastic Burgers Equation