Many models in engineering and physical sciences can be explained and approximated using the probabilistic and statistical tools. Constructions of optimal estimates as well as powerful goodness of fit tests represent main objects of our investigation. In particular, we are concentrated on developing efficient procedures for recovering unobserved functions and probability distributions in ill-posed and statistical inverse problems, like deconvolution, demixing and error-in variable models. The famous classical moment problem and the problem of numerical approximation of the radon transform inversion have a various applications in different fields including the image analysis and Computer Tomography.
- Robert Mnatsakanov: Statistical Inverse Problems, The Hausdorff and Stieltjes Moment Problems, Applications of Atatistical Methods in Actuarial and Financial Mathematics