Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions

Röckner M, Zhu R, Zhu X (2015)
Nonlinear Analysis Theory Methods & Applications 125: 358-397.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Röckner, MichaelUniBi; Zhu, Rongchan; Zhu, Xiangchan
Abstract / Bemerkung
In this paper, we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions, which can be applied to a large class of SPDE with finite delays, e.g. d-dimensional stochastic fractional Navier-Stokes equations with delays, d-dimensional stochastic reaction-diffusion equations with delays, d-dimensional stochastic porous media equations with delays. Moreover, under local monotonicity conditions for the nonlinear terms we obtain the existence and uniqueness of strong solutions to SPDE with delays. (C) 2015 Elsevier Ltd. All rights reserved.
Stichworte
equations with delay; Stochastic partial differential; Martingale problem; Local monotonicity; Stochastic functional equation
Erscheinungsjahr
2015
Zeitschriftentitel
Nonlinear Analysis Theory Methods & Applications
Band
125
Seite(n)
358-397
ISSN
0362-546X
Page URI
https://pub.uni-bielefeld.de/record/2772441

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Röckner M, Zhu R, Zhu X. Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions. Nonlinear Analysis Theory Methods & Applications. 2015;125:358-397.
Röckner, M., Zhu, R., & Zhu, X. (2015). Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions. Nonlinear Analysis Theory Methods & Applications, 125, 358-397. doi:10.1016/j.na.2015.05.019
Röckner, M., Zhu, R., and Zhu, X. (2015). Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions. Nonlinear Analysis Theory Methods & Applications 125, 358-397.
Röckner, M., Zhu, R., & Zhu, X., 2015. Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions. Nonlinear Analysis Theory Methods & Applications, 125, p 358-397.
M. Röckner, R. Zhu, and X. Zhu, “Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions”, Nonlinear Analysis Theory Methods & Applications, vol. 125, 2015, pp. 358-397.
Röckner, M., Zhu, R., Zhu, X.: Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions. Nonlinear Analysis Theory Methods & Applications. 125, 358-397 (2015).
Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. “Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions”. Nonlinear Analysis Theory Methods & Applications 125 (2015): 358-397.

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