Inverse problems for stochastic partial differential equations: some progresses and open problems

Cites Work

Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Some sufficient conditions for the controllability of wave equations with variable coefficients
Inverse problem for the wave equation with a white noise source
A weighted identity for stochastic partial differential operators and its applications
Determination of two unknowns simultaneously for stochastic Euler-Bernoulli beam equations
Unique continuation for stochastic parabolic equations
A quantitative internal unique continuation for stochastic parabolic equations
The analysis of linear partial differential operators. IV: Fourier integral operators
Stochastic partial differential equations. A modeling, white noise functional approach
Non-unicité du problème de Cauchy
Correlation based passive imaging with a white noise source
A quantitative boundary unique continuation for stochastic parabolic equations
Lipschitz stability for a semi-linear inverse stochastic transport problem
On recent progress of single-realization recoveries of random Schrödinger systems
An inverse source problem for the stochastic wave equation
Determining a random Schrödinger operator: both potential and source are random
Inverse problems and Carleman estimates. Global uniqueness, global convergence and experimental data
Estimation and control problems for stochastic partial differential equations
Stochastic ordinary and stochastic partial differential equations. Transition from microscopic to macroscopic equations.
Regularization of the backward stochastic heat conduction problem
Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems
An internal observability estimate for stochastic hyperbolic equations
Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems
Conditional stability in determination of initial data for stochastic parabolic equations
A unified controllability/observability theory for some stochastic and deterministic partial differential equations
Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems
Passive Sensor Imaging Using Cross Correlations of Noisy Signals in a Scattering Medium
Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem
Determination of two kinds of sources simultaneously for a stochastic wave equation
Null Controllability for Forward and Backward Stochastic Parabolic Equations
Optimal Measurement Methods for Distributed Parameter System Identification
Carleman and Observability Estimates for Stochastic Wave Equations
Control in an Information Rich World
Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems
A mathematical framework for stochastic climate models
Observability Estimate for Stochastic Schrödinger Equations and Its Applications
An inverse random source problem in a stochastic fractional diffusion equation
On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system
Carleman Estimates of Refined Stochastic Beam Equations and Applications
Determination of the solution of a stochastic parabolic equation by the terminal value
Inverse Source Problems for the Stochastic Wave Equations: Far-Field Patterns
Null controllability and inverse source problem for stochastic Grushin equation with boundary degeneracy and singularity
Inverse Problems
Mathematical Control Theory for Stochastic Partial Differential Equations
Carleman Estimates for Second Order Partial Differential Operators and Applications
Unique continuation for stochastic heat equations
Global Uniqueness for an Inverse Stochastic Hyperbolic Problem with Three Unknowns
Data Assimilation
Global Carleman estimate for stochastic parabolic equations, and its application
Observability Estimate and State Observation Problems for Stochastic Hyperbolic Equations
Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift
Local state observation for stochastic hyperbolic equations
Stochastic Equations in Infinite Dimensions