Markov Chains pp 167-193 | Cite as

Lyapunov Functions and Martingales

  • Pierre Brémaud
Part of the Texts in Applied Mathematics book series (TAM, volume 31)


The present chapter contains a potpourri of topics around potential theory and martingale theory. More exactly, it is a brief introduction to these topics, with the limited purpose of showing the power of martingale theory and the rich interplay between probability and analysis. An important aspect of this chapter concerns the various results complementing the study of recurrence of Chapter 3. In this respect, the single most important result is Foster’s theorem below.


Lyapunov Function Transition Matrix Repair Shop Martingale Theory Symmetric Random Walk 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Pierre Brémaud
    • 1
  1. 1.Laboratoire des Signaux et SystèmesCNRS-ESEGif-sur-YvetteFrance

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