By Sophia L. Kalpazidou

This ebook is a prototype delivering new perception into Markovian dependence through the cycle decompositions. It provides a scientific account of a category of stochastic methods often called cycle (or circuit) procedures - so-called simply because they're outlined through directed cycles. those tactics have distinctive and demanding houses in the course of the interplay among the geometric homes of the trajectories and the algebraic characterization of the Markov procedure. a massive software of this method is the perception it presents to electric networks and the duality precept of networks. particularly, it offers a wholly new method of endless electric networks and their functions in subject matters as diversified as random walks, the class of Riemann surfaces, and to operator theory.

The moment variation of this e-book provides new advances to many instructions, which demonstrate wide-ranging interpretations of the cycle representations like homologic decompositions, orthogonality equations, Fourier sequence, semigroup equations, and disintegration of measures. the flexibility of those interpretations is therefore inspired by means of the life of algebraic-topological ideas within the basics of the cycle representations. This ebook includes bankruptcy summaries in addition to a few distinctive illustrations.

Review of the sooner edition:

"This is a really beneficial monograph which avoids prepared methods and opens new learn views. it is going to definitely stimulate additional paintings, in particular at the interaction of algebraic and geometrical features of Markovian dependence and its generalizations."

Math Reviews.

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