1. Markovianity and ergodicity for a surface growth PDE
- Author
-
Franco Flandoli, Marco Romito, Dirk Blömker, Blömker, Dirk, Flandoli, Franco, and Romito, Marco
- Subjects
Statistics and Probability ,weak energy solution ,strong Feller property ,surface growth model ,weak energy solutions ,Markov solutions ,ergodicity ,FOS: Physical sciences ,Markov solution ,Feller-Prozess ,Markov-Prozess ,Schwache Lösung ,Probability theory ,Ergodentheorie ,35R60 ,FOS: Mathematics ,Applied mathematics ,Uniqueness ,ddc:510 ,Mathematical Physics ,Mathematics ,60H15 ,35Q99, 35R60, 60H30 ,Partial differential equation ,Wachstumsmodell ,Mathematical analysis ,Ergodicity ,Probability (math.PR) ,Mathematical Physics (math-ph) ,35Q99 ,Partielle Differentialgleichung ,Markov property ,Invariant measure ,Statistics, Probability and Uncertainty ,Martingale (probability theory) ,60H30 ,Surface growth model ,Mathematics - Probability - Abstract
The paper analyses a model in surface growth, where uniqueness of weak solutions seems to be out of reach. We provide the existence of a weak martingale solution satisfying energy inequalities and having the Markov property. Furthermore, under non-degeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure., Comment: 33 pages, 1 figure
- Published
- 2009