Abstract
We prove the existence and uniqueness of invariante measures for the fractional stochastic Burgers equation (FSBE) driven by the fractional power of the Laplacian and space-time white noise. We show also that the transition measures of the solution converge to the invariante measure in the norm of total variation. To this end we show first two results which are of independent interest: that the semigroup corresponding to the solution of the FSBE is strong Feller and irreducible.
Original language | English |
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Pages (from-to) | 145-174 |
Number of pages | 30 |
Journal | Global and Stochastic Analysis |
Volume | 1 |
Issue number | 2 |
Publication status | Published - Dec 2011 |
Keywords
- Fractional stochastic partial differential equations, ergodic properties, invariant measure, strong Feller property, cylindrical Wiener noise.