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. (preprint elettronico: http://arxiv.org/abs/math.PR/0611021)
Markovianity and ergodicity for a surface growth PDE / D. BLOEMKER; F. FLANDOLI; M. ROMITO. - In: ANNALS OF PROBABILITY. - ISSN 0091-1798. - STAMPA. - vol. 37, nr. 1:(2009), pp. 275-313. [doi:10.1214/08-AOP403]
Markovianity and ergodicity for a surface growth PDE
ROMITO, MARCO
2009
Abstract
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. (preprint elettronico: http://arxiv.org/abs/math.PR/0611021)
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