scholarly journals Inverse Problem Stability of a Continuous-in-Time Financial Model

2019 ◽  
Vol 39 (5) ◽  
pp. 1423-1439
Author(s):  
Tarik Chakkour
Keyword(s):  
Inverse Problem ◽  
Financial Model ◽  
Problem Stability

scholarly journals Inverse Problem: Stability for the aligned magnetic field by the Dirichlet-to-Neumann map for the wave equation in a periodic quantum waveguide

2016 ◽  
Vol Volume 23 - 2016 - Special... ◽  
Author(s):  
Mejri Youssef
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Wave Equation ◽  
Stability Estimate ◽  
Quantum Waveguide ◽  
Magnetic Wave ◽  
Problem Stability ◽  
Problème Inverse ◽  
Dirichlet To Neumann Map ◽  
Aligned Magnetic Field

International audience Dans ce papier, on a prouvé une estimation de stabilité pour le problème inverse de dé-termination du champ magnétique dans l'équation des ondes donné sur un domaine non borné à partir de l'opérateur de Dirichlet-to-Neumann. On a montré un résultat de stabilité pour ce problème inverse, dont la démonstration est basée sur la construction de solutions optique géométrique pour l'équation des ondes avec un potentiel magnétique 1-périodique. ABSTRACT. We consider the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic wave equation in a periodic quantum cylindrical waveguide from boundary observations. The observation is given by the Dirichlet to Neumann map associated to the wave equation. We prove by means of the geometrical optics solutions of the magnetic wave equation that the knowledge of the Dirichlet-to-Neumann map determines uniquely the aligned magnetic field induced by a time independent and 1-periodic magnetic potential. We establish a Hölder-type stability estimate in the inverse problem.

Inverse problem for a multi-term fractional differential equation

2020 ◽  
Vol 23 (3) ◽  
pp. 799-821
Author(s):  
Muhammad Ali ◽  
Sara Aziz ◽  
Salman A. Malik
Keyword(s):  
Differential Equation ◽  
Inverse Problem ◽  
Fractional Differential Equation ◽  
Local Existence ◽  
Operational Calculus ◽  
Banach Fixed Point Theorem ◽  
Local Boundary ◽  
Fractional Differential ◽  
Problem Stability ◽  
Orthogonal Set

AbstractInverse problem for a family of multi-term time fractional differential equation with non-local boundary conditions is studied. The spectral operator of the considered problem is non-self-adjoint and a bi-orthogonal set of functions is used to construct the solution. The operational calculus approach has been used to obtain the solution of the multi-term time fractional differential equations. Integral type over-determination condition is considered for unique solvability of the inverse problem. Different estimates of multinomial Mittag-Leffler functions alongside Banach fixed point theorem are used to prove the unique local existence of the solution of the inverse problem. Stability of the solution of the inverse problem on the given datum is established.

scholarly journals Inverse problem and concentration method of a continuous-in-time financial model

2016 ◽  
Vol 03 (02) ◽  
pp. 1650016 ◽  
Author(s):  
Tarik Chakkour ◽  
Emmanuel Frénod
Keyword(s):  
Inverse Problem ◽  
Numerical Method ◽  
Mathematical Framework ◽  
Financial Strategy ◽  
Financial Model ◽  
Time Model ◽  
Concentration Method

In a continuous-in-time model, there is an important financial quantity called Loan which cannot be determined directly in terms of algebraic spending but has a major impact on the financial strategy. In this paper, we use a mathematical framework to discuss an inverse problem of determining the implied Loan Measure from Algebraic Spending Measure when it is possible. In addition, we build a numerical method to concentrate a measure as a sum of Dirac masses.

scholarly journals Some Notes about the Continuous-in-Time Financial Model

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Tarik Chakkour
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Schwartz Space ◽  
Public Institutions ◽  
Financial Model ◽  
Time Model ◽  
The Uniqueness Theorem

In this paper, we investigate the properties of operators in the continuous-in-time model which is designed to be used for the finances of public institutions. These operators are involved in the inverse problem of this model. We discuss this inverse problem in Schwartz space that we prove the uniqueness theorem.

AN INVERSE PROBLEM IN THE DYNAMICAL REATOR THEORY

1982 ◽  
Vol 2 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Dexing Feng ◽  
Guangtian Zhu
Keyword(s):  
Inverse Problem

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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