Mixed time scale recursive algorithms

In this paper we investigate the behavior of certain types of mixed time scale adaptive algorithms. These systems comprise a \fast" or quickly changing algorithm mutually coupled to a \slow" or slowly changing algorithm. They arise naturally in a variety of adaptive environments such as in IIR system identi cation, the training of recurrent neural networks, decision feedback equalization, and others. (These algorithms (despite their title) should not be confused with the mixed time scales of wavelet transforms or other algorithms associated with multiresolution signal processing.) We give conditions for when the system can be analyzed from the framework of a simpler \frozen state" system. This analysis extends some of the previous work of V. Solo and his coworkers. EDICS 4.3.1,4.3.2,6.1.1,6.1.4 Permission granted to publish this abstract separately. 2