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Weak martingale solutions for the stochastic nonlinear Schrödinger equation driven by pure jump noise

Brzezniak, Zdzisław; Hornung, Fabian; Manna, Utpal

We construct a martingale solution of the stochastic nonlinear Schrödinger equation with a multiplicative noise of jump type in the Marcus canonical form. The problem is formulated in a general framework that covers the subcritical focusing and defocusing stochastic NLS in H1 on compact manifolds and on bounded domains with various boundary conditions. The proof is based on a variant of the Faedo-Galerkin method. In the formulation of the approximated equations, finite dimensional operators derived from the Littlewood-Paley decomposition complement the classical orthogonal projections to guarantee uniform estimates. Further ingredients of the construction are tightness criteria in certain spaces of càdlàg functions and Jakubowski’s generalization of the Skorohod-Theorem to nonmetric spaces.

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DOI: 10.5445/IR/1000085150
Veröffentlicht am 07.08.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000085150
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 47 S.
Serie CRC 1173 ; 2018/11
Schlagwörter nonlinear Schrödinger equation, weak martingale solutions, Marcus canonical form, Lévy noise, Littlewood-Paley decomposition
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