A Lévy process is observed at time points of distance delta until time T. We construct an estimator of the Lévy-Khinchine characteristics of the process and derive optimal rates of convergence simultaneously in T and delta. Thereby, we encompass the usual low- and high-frequency assumptions...

Given a networkN=(V,A,c), a sources εV, a. sinkt εV and somes —t cuts and suppose each element of the capacity vectorc can be changed with a cost proportional to the changes, the inverse problem of minimum cuts we study here is to change the original capacities with the least total cost...

This work investigates the inverse problem of reconstructing a spacewise dependent heat source in the parabolic heat equation using a final temperature measurement. Such problem has important application in a large field of applied science. On the basis of the optimal control framework, the...

This paper presents an iterative alternating algorithm for solving an inverse problem in linear elasticity. A relaxation procedure is developed in order to increase the rate of convergence of the algorithm and two selection criteria for the variable relaxation factors are provided. The boundary...

We consider the inverse problem of identifying a Robin coefficient by performing measurement on some part of the boundary. After turning the inverse problem to an optimisation one by using a Kohn and Vogelius cost function, we study the stability of this method and present some numericals...

Mathematical model of vertical electrical sounding by using resistivity method is studied. The model leads to an inverse problem of determination of the unknown leading coefficient (conductivity) of the elliptic equation in R2 in a slab. The direct problem is obtained in the form of mixed BVP in...

An inverse problem is formulated to determine water capacity of porous media. Mathematical model of the problem involves a nonlinear parabolic equation in which the coefficient representing water capacity is unknown and to be determined from over specified data measured on the boundary. By using...