Variational solutions to nonlinear stochastic differential equations in Hilbert spaces

Barbu V, Röckner M (2018)
Stochastics and Partial Differential Equations: Analysis and Computations 6(3): 500-524.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
Barbu, Viorel; Röckner, MichaelUniBi
Abstract / Bemerkung
One introduces a new variational concept of solution for the stochastic differential equation ; in a real Hilbert space where , is a maximal monotone subpotential operator in H while W is a Wiener process in H on a probability space . In this new context, the solution exists for each , is unique, and depends continuously on x. This functional scheme applies to a general class of stochastic PDE so far not covered by the classical variational existence theory (Krylov and Rozovskii in J Sov Math 16:1233-1277, 1981; Liu and Rockner in Stochastic partial differential equations: an introduction, Springer, Berlin, 2015; Pardoux in Equations aux d,riv,es partielles stochastiques nonlin,aires monotones, ThSse, Orsay, 1972) and, in particular, to stochastic variational inequalities and parabolic stochastic equations with general monotone nonlinearities with low or superfast growth to +infinity.
Stichworte
Brownian motion; Maximal monotone operator; Subdifferential; Random; differential equation; Minimization problem
Erscheinungsjahr
2018
Zeitschriftentitel
Stochastics and Partial Differential Equations: Analysis and Computations
Band
6
Ausgabe
3
Seite(n)
500-524
ISSN
2194-0401
eISSN
2194-041X
Page URI
https://pub.uni-bielefeld.de/record/2931102

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Barbu V, Röckner M. Variational solutions to nonlinear stochastic differential equations in Hilbert spaces. Stochastics and Partial Differential Equations: Analysis and Computations. 2018;6(3):500-524.
Barbu, V., & Röckner, M. (2018). Variational solutions to nonlinear stochastic differential equations in Hilbert spaces. Stochastics and Partial Differential Equations: Analysis and Computations, 6(3), 500-524. doi:10.1007/s40072-018-0114-0
Barbu, V., and Röckner, M. (2018). Variational solutions to nonlinear stochastic differential equations in Hilbert spaces. Stochastics and Partial Differential Equations: Analysis and Computations 6, 500-524.
Barbu, V., & Röckner, M., 2018. Variational solutions to nonlinear stochastic differential equations in Hilbert spaces. Stochastics and Partial Differential Equations: Analysis and Computations, 6(3), p 500-524.
V. Barbu and M. Röckner, “Variational solutions to nonlinear stochastic differential equations in Hilbert spaces”, Stochastics and Partial Differential Equations: Analysis and Computations, vol. 6, 2018, pp. 500-524.
Barbu, V., Röckner, M.: Variational solutions to nonlinear stochastic differential equations in Hilbert spaces. Stochastics and Partial Differential Equations: Analysis and Computations. 6, 500-524 (2018).
Barbu, Viorel, and Röckner, Michael. “Variational solutions to nonlinear stochastic differential equations in Hilbert spaces”. Stochastics and Partial Differential Equations: Analysis and Computations 6.3 (2018): 500-524.