S. Kalpazidou

On multiple circuit chains with a countable infinity of states

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 Polyas 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.

Markov chains in Banach spaces on cycles

The problem of defining denumerable Markov chains by a countable infinity of weighted directed cycles is solved by using suitable Banach spaceslp on cycles and edges. Furthermore, it is showed that the transition probabilities of such chains may be described by Fourier series on orthonormal collections of homologic ingredients.

REPRESENTATION OF DENUMERABLE MARKOV CHAINS WITH MULTIPLE STATES BY WEIGHTED CIRCUITS

The constructive solution to the problem of representing a strictly stationary Markov chain C with a countable infinity of r- sequences (i,, i2, * , i,), r > 1, as states by a class of directed weighted circuits is given. Associating the chain C with its dual chain ?I having reversed states and the same transition law, a connection with physical laws that govern diffusion of electrical current through a directed planar network with r-series-connected nodes is shown.

Orthogonal cycle transforms of stochastic matrices

AbstractIn this paper we investigate new Fourier series with respect to orthonormal families of directed cyclesn

THE FORWARD AND BACKWARD ROTATIONAL DECOMPOSITIONS OF MARKOV CHAINS

gamma

Some asymptotic results on digits of the nearest integer continued fraction

n, which occur in the graph of a recurrent stochastic matrixP. Specifically, it is proved thatP may be approximated in a suitable Hilbert space by the Fourier seriesn

On beurling's inequality in terms of thermal power

sum {w_gamma } underline gamma