Cycle representations of Markov processes
By: Sophia L. Kalpazidou.
Series: Applications of mathematics ;; 28
Publisher: Springer-Verlag
Published: 1995
Place of publication: New York
Language: eng
Number of pages: 194
Subjects: Markov processes.; Algebraic cycles.
Description: This book presents an original and systematic account of a class of stochastic processes known as cycle (or circuit) processes, so called because they may be defined by directed cycles. These processes have special and important properties through the interaction between the geometric properties of the trajectories and the algebraic characterization of the finite-dimensional distributions.

An important application of this approach is the new insight it provides into Markovian dependence and electrical networks. In particular, it provides an entirely new approach to Markov processes and infinite electrical networks, and their applications in topics as diverse as random walks, ergodic theory, dynamical systems, potential theory, theory of matrices, algebraic topology, complexity theory, the classification of Riemann surfaces, and operator theory.

The author surveys the three principal developments in cycle theory: the cycle-decomposition formula and its relation to the Markov process; entropy production and how it may be used to measure how far a process is from being reversible; and how a finite recurrent stochastic matrix may be defined by a rotation of the circle and a partition whose elements consist of finite unions of circle-arcs.
Notes: Includes bibliographical references (p. 169-190) and index.