Stochastic regularization of the observability problem for the heat equation

An attempt is made to develop a stochastic approach to the study of inverse problems for linear and diffusion-type nonlinear parabolic evolution equations. It is suggested that these equations be approximated by a certain system of stochastic ordinary differential equations and that the inverse problems for this system be studied. The possibility of such an approximation is based on the hydrodynamic scaling limit.<>