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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	22
Journal	Nonlinear Differential Equations and Applications
Volume	26
Issue number	3
DOIs	https://doi.org/10.1007/s00030-019-0569-3
Publication status	Published - 1 Jun 2019
Externally published	Yes

Keywords

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

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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",

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

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AU - de Bouard, Anne

AU - Hausenblas, Erika

AU - Ondreját, Martin

PY - 2019/6/1

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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.

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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

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

Abstract

Keywords

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