On multiple circuit chains with a countable infinity of states

S. Kalpazidou

Stochastic Processes and their Applications, 1989, vol. 31, issue 1, 51-70

Abstract: Denumerable rth order circuit chains (r> 1) are defined as genuine denumerable Markov chains of order r with transition law expressed in terms of the weights of a denumerable class of overlapping directed circuits in the plane. Recurrence and stationarity of such chains are studied in connection with a suitable planar motion through a directed network with r-series-connected points as nodes. In particular a generalization of Pólya's theorem concerning random walks on multi-dimensional lattice-points is derived. We also show a relationship between the approach to denumerable Markov chains with multiple states defined by weighted circuits and diffusion of electrical current through a network.

Keywords: multiple; Markov; chains; directed; circuits; recurrence; stationarity; r-series-connected; nodes; electrical; current (search for similar items in EconPapers)
Date: 1989
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