The Annals of Probability

Markovianity and ergodicity for a surface growth PDE

Dirk Blömker, Franco Flandoli, and Marco Romito

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The paper analyzes a model in surface growth where the uniqueness of weak solutions seems to be out of reach. We prove existence of a weak martingale solution satisfying energy inequalities and having the Markov property. Furthermore, under nondegeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure.

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Ann. Probab., Volume 37, Number 1 (2009), 275-313.

First available in Project Euclid: 17 February 2009

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Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35Q99: None of the above, but in this section 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H30: Applications of stochastic analysis (to PDE, etc.)

Surface growth model weak energy solutions Markov solutions strong Feller property ergodicity


Blömker, Dirk; Flandoli, Franco; Romito, Marco. Markovianity and ergodicity for a surface growth PDE. Ann. Probab. 37 (2009), no. 1, 275--313. doi:10.1214/08-AOP403.

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