Coupling stochastic PDEs. (English) Zbl 1122.35383
Zambrini, Jean-Claude (ed.), XIVth international congress on mathematical physics (ICMP 2003), Lisbon, Portugal, 28 July – 2 August 2003. Selected papers based on the presentation at the conference. Hackensack, NJ: World Scientific (ISBN 981-256-201-X/hbk). 281-289 (2005).
Summary: We consider a class of parabolic stochastic PDEs driven by white noise in time, and we are interested in showing ergodicity for some cases where the noise is degenerate, i.e., acts only on part of the equation. In some cases where the standard strong Feller irreducibility argument fails, one can nevertheless implement a coupling construction that ensures uniqueness of the invariant measure. We focus on the example of the complex Ginzburg-Landau equation driven by real space-time white noise.
For the entire collection see [Zbl 1089.81005].
For the entire collection see [Zbl 1089.81005].
MSC:
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 47D07 | Markov semigroups and applications to diffusion processes |
