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Random Walks on ω-Networks

In: Harmonic Analysis and Discrete Potential Theory

Author

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  • A. H. Zemanian

    (State University of New York, Department of Electrial Engineering)

Abstract

A k-network, where k is any finite or transfinite, countable ordinal, is a transfinite generalization of an ordinary infinite electrical network. A prior work has established a theory for random walks on k-networks in the case where k is any natural number. The present work generalizes still further by establishing a theory for random walks on an ω-network, where ω is the first transfinite ordinal. It appears that such a theory can be established recursively for any ω-network by using the method of the prior work when proceeding to a successor ordinal and the method of the present work when proceeding to a limit ordinal.

Suggested Citation

  • A. H. Zemanian, 1992. "Random Walks on ω-Networks," Springer Books, in: Massimo A. Picardello (ed.), Harmonic Analysis and Discrete Potential Theory, pages 249-257, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2323-3_20
    DOI: 10.1007/978-1-4899-2323-3_20
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