Averaging Methods for the Asymptotic Analysis of Learning and Adaptive Systems, with Small Adjustment Rate. Analysis of Nonlinear Stochastic Systems with Wide-Band Inputs.
Abstract
Recently proved theorems concerning weak convergence of non-Markovian processes to diffusions, together with an averaging and a stability method, are applied to two (learning or adaptive) processes of current interest: (1) an automata model for route selection in telephone traffic routing, (2) an adaptive quantizer for use in the transmission of random signals in communication theory. The models are chosen because they are prototypes of a large class to which the methods can be applied. The technique of application of the basic theorems to such processes is developed. Suitably interpolated and normalized 'learning or adaptive' processes converge weakly to a diffusion, as the 'learning or adaptation' rate goes to zero. For small learning rate, the qualitative properties (e.g., asymptotic (large-time) variances and parametric dependence) of the processes can be determine from the properties of the limit. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1980
- Accession Number
- ADA087029
Entities
People
- Hai Huang
- Harold J. Kushner
- Y. Bar-ness
Organizations
- Brown University