The nonlinear Schrödinger equation driven by jump processes

DOI10.1016/j.jmaa.2019.02.036zbMath1480.60255arXiv1702.02523OpenAlexW2587764705MaRDI QIDQ2633733

Erika Hausenblas, Anne de Bouard

Publication date: 10 May 2019

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.02523

zbMATH Keywords

Lévy processesstochastic partial differential equationsnonlinear Schrödinger equationPoisson random measuresstochastic integral of jump type

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) NLS equations (nonlinear Schrödinger equations) (35Q55) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Jump processes on general state spaces (60J76) Nonlinear processes (e.g., (G)-Brownian motion, (G)-Lévy processes) (60G65)

Related Items (9)

The stochastic Strichartz estimates and stochastic nonlinear Schrödinger equations driven by Lévy noise ⋮ Invariant measure of stochastic damped Ostrovsky equation driven by pure jump noise ⋮ A large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise ⋮ The stochastic nonlinear Schrödinger equations driven by pure jump noise ⋮ Optimal bilinear control of stochastic nonlinear Schrödinger equations: mass-(sub)critical case ⋮ The stochastic nonlinear Schrödinger equation in unbounded domains and non-compact manifolds ⋮ Ergodicity of stochastic damped Ostrovsky equation driven by white noise ⋮ Weak martingale solutions for the stochastic nonlinear Schrödinger equation driven by pure jump noise ⋮ Uniqueness of the nonlinear Schrödinger equation driven by jump processes

Cites Work

• Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth
• Stochastic nonlinear Schrödinger equations with linear multiplicative noise: rescaling approach
• The nonlinear Schrödinger equation with white noise dispersion
• Stochastic reaction-diffusion equations driven by jump processes
• Blowup for the stochastic nonlinear Schrödinger equation with multiplicative noise
• A stochastic nonlinear Schrödinger equation with multiplicative noise
• On the Integrability of the Poisson Driven Stochastic Nonlinear Schrödinger Equations
• Uniqueness in Law of the Itô Integral with Respect to Lévy Noise
• Lévy Processes and Stochastic Calculus
• The Stochastic Nonlinear Schrödinger Equation inH¹
• Financial Modelling with Jump Processes
• Stochastic Partial Differential Equations with Levy Noise
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The nonlinear Schrödinger equation driven by jump processes