Texts in Applied Mathematics Volume 31, 1999, pp 167-193

Lyapunov Functions and Martingales

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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.