On invariance principles for distributed parameter identification algorithms
Volume 3, Issue 1 (1992), pp. 98–118
Pub. online: 1 January 1992
Type: Research Article
Research of this author was supported in part by the Air Force Office of Scientific Research under grant AFOSR-91-0021.
Published
1 January 1992
1 January 1992
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.