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Journal of the London Mathematical Society 2000 61(1):301-314; doi:10.1112/S0024610799008364
© 2000 by London Mathematical Society
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© The London Mathematical Society

The Markov Oscillation Problem in Discrete Time

Yonglong Dai and Eric Renshaw

Department of Mathematics, Zhongshan University Guangzhou 510275, China, stsdaiy{at}zsulink.zsu.edu.cn
Department of Statistics and Modelling Science, Livingstone Tower, University of Strathclyde 26 Richmond Street, Glasgow G1 1XH, eric{at}stams.strath.ac.uk

Received 6 March 1997. Revision received 23 July 1998.

Consider a discrete-time regenerative phenomenon with associated renewal sequence un. General results for the supremum of um+1, ..., um+n are developed for those renewal sequences {un} for which the first m + 1 elements match those of a fixed renewal sequence {vn}, that is, u0 = v0, ..., um = vm. A series of associated lemmas are developed in the process.


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