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Uniqueness of the nonlinear Schrödinger equation driven by jump processes

  • Anne de Bouard
  • Erika Hausenblas
  • Martin OndrejátEmail author
Article
  • 42 Downloads

Abstract

In a recent paper by the first two authors, existence of martingale solutions to a stochastic nonlinear Schrödinger equation driven by a Lévy noise was proved. In this paper, we prove pathwise uniqueness, uniqueness in law and existence of strong solutions to this problem using an abstract uniqueness result of Kurtz.

Keywords

Uniqueness results Yamada–Watanabe–Kurtz theorem Stochastic integral of jump type Stochastic partial differential equations Poisson random measures Lévy processes Schrödinger equation 

Mathematics Subject Classification

Primary 60H15 Secondary 60G57 

Notes

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Authors and Affiliations

  1. 1.CMAP, Ecole Polytechnique, CNRSUniversité Paris-SaclayPalaiseauFrance
  2. 2.Lehrstuhl Angewandte MathematikMontanuniversität LeobenLeobenAustria
  3. 3.The Czech Academy of Sciences, Institute of Information Theory and AutomationPrague 8Czech Republic

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