Affiliations: Department of Mathematics, Wayne State University, Detroit, MI 48202, USA | Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
Note: [] Research of this author was supported in part by the National Science Foundation under grant DMS-9022139.
Note: [] Research of this author was supported in part by the Air Force Office of Scientific Research under grant AFOSR-91-0021.
Abstract: We consider a class of identification algorithms for distributed parameter systems. Utilizing stochastic optimization techniques, sequences of estimators are constructed by minimizing appropriate functionals. The main effort is to develop weak and strong invariance principles for the underlying algorithms. By means of weak convergence methods, a functional central limit theorem is established. Using the Skorohod imbedding, a strong invariance principle is obtained. These invariance principles provide very precise rates of convergence results for parameter estimates, yielding important information for experimental design.
