Random Processes and Learning
ISBN:
978-3-642-46186-6
Auflage:
Softcover reprint of the original 1st ed. 1969
Verlag:
Springer Berlin
Land des Verlags:
Deutschland
Erscheinungsdatum:
25.02.2012
Reihe:
Grundlehren der mathematischen Wissenschaften
Format:
Softcover
Seitenanzahl:
308
Lieferung in 5-10 Werktagen
Versandkostenfrei ab 40 Euro in Österreich
The aim of" the present monograph is two-fold: (a) to give a short account of the main results concerning the theory of random systems with complete connections, and (b) to describe the general learning model by means of random systems with complete connections. The notion of chain with complete connections has been introduced in probability theory by ONICESCU and MIHOC (1935a). These authors have set themselves the aim to define a very broad type of dependence which takes into account the whole history of the evolution and thus includes as a special case the Markovian one. In a sequel of papers of the period 1935-1937, ONICESCU and MIHOC developed the theory of these chains for the homogeneous case with a finite set of states from differ ent points of view: ergodic behaviour, associated chain, limit laws. These results led to a chapter devoted to these chains, inserted by ONI CESCU and MIHOC in their monograph published in 1937. Important contributions to the theory of chains with complete connections are due to DOEBLIN and FORTET and refer to the period 1937-1940. They consist in the approach of chains with an infinite history (the so-called chains of infinite order) and in the use of methods from functional analysis.
