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Introduction

  • Yuri Kifer
Part of the Progress in Probability and Statistics book series (PRPR, volume 10)

Abstract

Ergodic theory of dynamical systems i.e., the qualitative analysis of iterations of a single transformation is nowadays a well developed theory. In 1945 S. Ulam and J. von Neumann in their short note [44] suggested to study ergodic theorems for the more general situation when one applies in turn different transformations chosen at random. Their program was fulfilled by S. Kakutani [23] in 1951. ‘Both papers considered the case of transformations with a common invariant measure. Recently Ohno [38] noticed that this condition was excessive. Ergodic theorems are just the beginning of ergodic theory. Among further major developments are the notions of entropy and characteristic exponents.

Keywords

Markov Chain Ergodic Theory Ergodic Theorem Characteristic Exponent Stochastic Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston, Inc. 1986

Authors and Affiliations

  • Yuri Kifer
    • 1
  1. 1.Institute of Mathematics and Computer ScienceJerusalemIsrael

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