A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations

Röckner M, Sobol Z (2004)
Comptes Rendus Mathematique 338(12): 945-949.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We develop a new method to uniquely solve a large class of heat equations, so called Kolmogorov equations in infinitely many variables. The equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper (Lyapunov type) functions. In this way, for the first time, the solutions are constructed everywhere without exceptional sets for equations with possibly non-locally Lipschitz drifts. Apart from general analytic interest, the main motivation is to apply this to uniquely solve martingale problems in the sense of Stroock-Varadhan given by stochastic partial differential equations from hydrodynamics, such as the stochastic Navier-Stokes equations. In this Note this is done in the case of the stochastic generalized Burgers equation. Uniqueness is shown in the sense of Markov flows. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.
Erscheinungsjahr
2004
Zeitschriftentitel
Comptes Rendus Mathematique
Band
338
Ausgabe
12
Seite(n)
945-949
ISSN
1631-073X
Page URI
https://pub.uni-bielefeld.de/record/1607633

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Röckner M, Sobol Z. A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations. Comptes Rendus Mathematique. 2004;338(12):945-949.
Röckner, M., & Sobol, Z. (2004). A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations. Comptes Rendus Mathematique, 338(12), 945-949. doi:10.1016/j.crma.2004.03.024
Röckner, M., and Sobol, Z. (2004). A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations. Comptes Rendus Mathematique 338, 945-949.
Röckner, M., & Sobol, Z., 2004. A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations. Comptes Rendus Mathematique, 338(12), p 945-949.
M. Röckner and Z. Sobol, “A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations”, Comptes Rendus Mathematique, vol. 338, 2004, pp. 945-949.
Röckner, M., Sobol, Z.: A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations. Comptes Rendus Mathematique. 338, 945-949 (2004).
Röckner, Michael, and Sobol, Zeev. “A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations”. Comptes Rendus Mathematique 338.12 (2004): 945-949.