Orthogonal cycle transforms of stochastic matrices |
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| Authors: | S Kalpazidou Joel E Cohen |
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| Affiliation: | (1) Department of Mathematics, Aristotle University of Thessaloniki, 54 006 Thessaloniki, Greece;(2) Laboratory of Populations, Rockefeller University, 1230 York Avenue, Box 20, 10021-6399 New York, New York;(3) Columbia University, 10027 New York, NY |
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| Abstract: | In this paper we investigate new Fourier series with respect to orthonormal families of directed cycles
, 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 series
. This approach provides a proof in terms of Hilbert space of the cycle decomposition formula for finite stochastic matricesP. |
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