STOCHASTIC QUASI-GEOSTROPHIC EQUATION

Röckner M, Zhu R, Zhu X (2012)
Infinite Dimensional Analysis Quantum Probability and Related Topics 15(1): 1250001.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Abstract / Bemerkung
In this note we study the 2D stochastic quasi-geostrophic equation in T-2 for general parameter alpha is an element of (0, 1) and multiplicative noise. We prove the existence of martingale solutions and pathwise uniqueness under some condition in the general case, i.e. for all alpha is an element of (0,1). In the subcritical case alpha > 1/2, we prove existence and uniqueness of (probabilistically) strong solutions and construct a Markov family of solutions. In particular, it is uniquely ergodic for alpha > 2/3 provided the noise is non-degenerate. In this case, the convergence to the (unique) invariant measure is exponentially fast. In the general case, we prove the existence of Markov selections.
Stichworte
strong Feller property; Markov selections; ergodicity; well posedness; Stochastic quasi-geostrophic; property; martingale problem; Markov
Erscheinungsjahr
2012
Zeitschriftentitel
Infinite Dimensional Analysis Quantum Probability and Related Topics
Band
15
Ausgabe
1
Art.-Nr.
1250001
ISSN
0219-0257
Page URI
https://pub.uni-bielefeld.de/record/2501923

Zitieren

Röckner M, Zhu R, Zhu X. STOCHASTIC QUASI-GEOSTROPHIC EQUATION. Infinite Dimensional Analysis Quantum Probability and Related Topics. 2012;15(1): 1250001.
Röckner, M., Zhu, R., & Zhu, X. (2012). STOCHASTIC QUASI-GEOSTROPHIC EQUATION. Infinite Dimensional Analysis Quantum Probability and Related Topics, 15(1), 1250001. doi:10.1142/S0219025712500014
Röckner, M., Zhu, R., and Zhu, X. (2012). STOCHASTIC QUASI-GEOSTROPHIC EQUATION. Infinite Dimensional Analysis Quantum Probability and Related Topics 15:1250001.
Röckner, M., Zhu, R., & Zhu, X., 2012. STOCHASTIC QUASI-GEOSTROPHIC EQUATION. Infinite Dimensional Analysis Quantum Probability and Related Topics, 15(1): 1250001.
M. Röckner, R. Zhu, and X. Zhu, “STOCHASTIC QUASI-GEOSTROPHIC EQUATION”, Infinite Dimensional Analysis Quantum Probability and Related Topics, vol. 15, 2012, : 1250001.
Röckner, M., Zhu, R., Zhu, X.: STOCHASTIC QUASI-GEOSTROPHIC EQUATION. Infinite Dimensional Analysis Quantum Probability and Related Topics. 15, : 1250001 (2012).
Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. “STOCHASTIC QUASI-GEOSTROPHIC EQUATION”. Infinite Dimensional Analysis Quantum Probability and Related Topics 15.1 (2012): 1250001.