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.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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.
Erscheinungsjahr
Zeitschriftentitel
Stochastic Processes and their Applications
Band
119
Ausgabe
5
Seite(n)
1725-1764
ISSN
PUB-ID

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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. doi: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.