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

Zdzislaw Brzezniak, Fabian Hornung, Utpal Manna

Research output: Contribution to journalArticlepeer-review


We construct a martingale solution of the stochastic nonlinear Schrödinger equation
(NLS) 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 H^1 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.
Original languageEnglish
Number of pages53
JournalStochastic Partial Differential Equations: Analysis and Computations
Early online date16 May 2019
Publication statusE-pub ahead of print - 16 May 2019

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  • Nonlinear Schrödinger equation
  • Weak martingale solutions
  • Marcus canonical form
  • Lévy noise
  • Littlewood–Paley decomposition

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