Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise

DOI10.1214/17-AOP1217zbMath1431.60053arXiv1607.06652MaRDI QIDQ1660624

Deng Zhang, Viorel Barbu, Michael Roeckner

Publication date: 16 August 2018

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.06652

zbMATH Keywords

optimal controlWiener processnonlinear Schrödinger equationbackward stochastic equation

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (20)

The stochastic Strichartz estimates and stochastic nonlinear Schrödinger equations driven by Lévy noise ⋮ Strichartz and Local Smoothing Estimates for Stochastic Dispersive Equations with Linear Multiplicative Noise ⋮ Centralized systemic risk control in the interbank system: weak formulation and gamma-convergence ⋮ Quantum mean-field games ⋮ Scattering for stochastic nonlinear Schrödinger equations ⋮ Large Sample Mean-Field Stochastic Optimization ⋮ Multi solitary waves to stochastic nonlinear Schrödinger equations ⋮ Optimal Control for Stochastic Nonlinear Schrödinger Equation on Graph ⋮ Multi-bubble Bourgain-Wang solutions to nonlinear Schrödinger equations ⋮ Stochastic nonlinear Schrödinger equations in the defocusing mass and energy critical cases ⋮ Optimal bilinear control of stochastic nonlinear Schrödinger equations: mass-(sub)critical case ⋮ Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces ⋮ Optimal control results for a class of stochastic Schrödinger equations ⋮ The stochastic nonlinear Schrödinger equation in unbounded domains and non-compact manifolds ⋮ Analysis and optimal velocity control of a stochastic convective Cahn-Hilliard equation ⋮ The law of large numbers for quantum stochastic filtering and control of many-particle systems ⋮ Optimal Distributed Control of a Stochastic Cahn--Hilliard Equation ⋮ Optimal control of stochastic phase-field models related to tumor growth ⋮ Construction of minimal mass blow-up solutions to rough nonlinear Schrödinger equations ⋮ On uniqueness of multi-bubble blow-up solutions and multi-solitons to \(L^2\)-critical nonlinear Schrödinger equations

Cites Work

• Unnamed Item
• Unnamed Item
• Stochastic nonlinear Schrödinger equations
• Stochastic partial differential equations: an introduction
• Stochastic nonlinear Schrödinger equations with linear multiplicative noise: rescaling approach
• Implicit Lyapunov control of finite dimensional Schrödinger equations
• Strichartz estimates and local smoothing estimates for asymptotically flat Schrödinger equations
• Quantum trajectories and measurements in continuous time. The diffusive case
• Compact sets in the space \(L^ p(0,T;B)\)
• A stochastic nonlinear Schrödinger equation with multiplicative noise
• On the variational principle
• Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control
• Existence of strong solutions for Itô's stochastic equations via approximations
• Stochastic nonlinear Schrödinger equations: no blow-up in the non-conservative case
• Lyapunov control of bilinear Schrödinger equations
• Optimal Bilinear Control of Gross--Pitaevskii Equations
• Multigrid Optimization Schemes for Solving Bose–Einstein Condensate Control Problems
• Nonconvex minimization problems
• Adapted solution of a backward semilinear stochastic evolution equation
• Directionally Lipschitzian Functions and Subdifferential Calculus
• Existence, uniqueness and space regularity of the adapted solutions of a backward spde
• The Stochastic Nonlinear Schrödinger Equation inH¹
• Stochastic Equations in Infinite Dimensions
• Remarks on damped fractional Schrödinger equation with pure power nonlinearity
• Optimal Bilinear Control of an Abstract Schrödinger Equation
• On Nearest Points of Sets in Uniformly Convex Banach Spaces
• Introduction to nonlinear dispersive equations

This page was built for publication: Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise