Uniqueness of the nonlinear Schrödinger equation driven by jump processes

Anne de Bouard; Erika Hausenblas; Martin Ondreját

doi:10.1007/s00030-019-0569-3

Uniqueness of the nonlinear Schrödinger equation driven by jump processes

Anne de Bouard
, Erika Hausenblas
, Martin Ondreját

Université Paris-Saclay
Montanuniversitaet Leoben
Institute of Information Theory and Automation of the Academy of Sciences of the Czech Republic

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Numéro d'article	22
journal	Nonlinear Differential Equations and Applications
Volume	26
Numéro de publication	3
Les DOIs	https://doi.org/10.1007/s00030-019-0569-3
état	Publié - 1 juin 2019
Modification externe	Oui

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10.1007/s00030-019-0569-3

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title = "Uniqueness of the nonlinear Schr{\"o}dinger equation driven by jump processes",

abstract = "In a recent paper by the first two authors, existence of martingale solutions to a stochastic nonlinear Schr{\"o}dinger equation driven by a L{\'e}vy 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 = "L{\'e}vy processes, Poisson random measures, Schr{\"o}dinger equation, Stochastic integral of jump type, Stochastic partial differential equations, Uniqueness results, Yamada–Watanabe–Kurtz theorem",

author = "\{de Bouard\}, Anne and Erika Hausenblas and Martin Ondrej{\'a}t",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

year = "2019",

month = jun,

day = "1",

doi = "10.1007/s00030-019-0569-3",

language = "English",

volume = "26",

journal = "Nonlinear Differential Equations and Applications",

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T1 - Uniqueness of the nonlinear Schrödinger equation driven by jump processes

AU - de Bouard, Anne

AU - Hausenblas, Erika

AU - Ondreját, Martin

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

KW - Lévy processes

KW - Poisson random measures

KW - Schrödinger equation

KW - Stochastic integral of jump type

KW - Stochastic partial differential equations

KW - Uniqueness results

KW - Yamada–Watanabe–Kurtz theorem

UR - https://www.scopus.com/pages/publications/85067052020

U2 - 10.1007/s00030-019-0569-3

DO - 10.1007/s00030-019-0569-3

M3 - Article

AN - SCOPUS:85067052020

SN - 1021-9722

VL - 26

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 3

M1 - 22

ER -

Uniqueness of the nonlinear Schrödinger equation driven by jump processes

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