An important class of structural econometric models (nonlinear rational expectations, option pricing, auction models, ...) characterize observable variables as highly nonlinear transforma- tions of some latent variables. These transformations are one-to-one, but they depend on the unknown...

We prove that there exists a gain function (η(t),β(t))t⩾0 such that the solution of the SDE dxt=η(t)(−gradU(xt)dt+β(t)dBt) ‘settles’ down on the set of global minima of U. In particular, the existence of a gain function (η(t))t⩾0 so that yt satisfying dyt=η(t)(−gradU(yt)dt+dBt)...