On the Controllability Problem Arising in Financial Mathematics

This paper deals with the approximate controllability problem for a parabolic equation defined for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x \in \mathbb{R},{\text{ }}t \in \;[0,T]$$ \end{document}. It is possible to find a sequence of initial conditions with given compact support such that traces at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x = 0$$ \end{document} of corresponding solutions converge to the trace of a given solution. We obtain estimates of the rate of this convergence. These estimates are constructed in terms of eigenvalues of certain compact operator.