Martingale solutions and Markov selections for stochastic partial differential equations

Goldys B, Röckner M, Zhang X (2009)
Stochastic Processes and their Applications 119(5): 1725-1764.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We present a general framework for solving stochastic porous medium equations and stochastic Navier-Stokes equations in the sense of martingale solutions. Following Krylov [N.V. Krylov, The selection of a Markov process from a Markov system of processes, and the construction of quasidiffusion processes, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 691-708] and Flandoli-Romito [F. Flandoli, N. Romito, Markov selections for the 3D stochastic Navier-Stokes equations, Probab. Theory Related Fields 140 (2008) 407-458], we also study the existence of Markov selections for stochastic evolution equations in the absence of uniqueness. (C) 2008 Elsevier B.V. All rights reserved.
Stichworte
Markov selection; Stochastic porous medium; equation; Stochastic Navier-Stokes equation; Martingale solution
Erscheinungsjahr
2009
Zeitschriftentitel
Stochastic Processes and their Applications
Band
119
Ausgabe
5
Seite(n)
1725-1764
ISSN
0304-4149
Page URI
https://pub.uni-bielefeld.de/record/1634128

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Goldys B, Röckner M, Zhang X. Martingale solutions and Markov selections for stochastic partial differential equations. Stochastic Processes and their Applications. 2009;119(5):1725-1764.
Goldys, B., Röckner, M., & Zhang, X. (2009). Martingale solutions and Markov selections for stochastic partial differential equations. Stochastic Processes and their Applications, 119(5), 1725-1764. https://doi.org/10.1016/j.spa.2008.08.009
Goldys, B., Röckner, M., and Zhang, X. (2009). Martingale solutions and Markov selections for stochastic partial differential equations. Stochastic Processes and their Applications 119, 1725-1764.
Goldys, B., Röckner, M., & Zhang, X., 2009. Martingale solutions and Markov selections for stochastic partial differential equations. Stochastic Processes and their Applications, 119(5), p 1725-1764.
B. Goldys, M. Röckner, and X. Zhang, “Martingale solutions and Markov selections for stochastic partial differential equations”, Stochastic Processes and their Applications, vol. 119, 2009, pp. 1725-1764.
Goldys, B., Röckner, M., Zhang, X.: Martingale solutions and Markov selections for stochastic partial differential equations. Stochastic Processes and their Applications. 119, 1725-1764 (2009).
Goldys, Benjamin, Röckner, Michael, and Zhang, Xicheng. “Martingale solutions and Markov selections for stochastic partial differential equations”. Stochastic Processes and their Applications 119.5 (2009): 1725-1764.

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