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The Markov Oscillation Problem in Discrete Time
Author(s) -
Dai Yonglong,
Renshaw Eric
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799008364
Subject(s) - sequence (biology) , infimum and supremum , renewal theory , markov chain , markov renewal process , discrete time and continuous time , series (stratigraphy) , oscillation (cell signaling) , mathematics , process (computing) , markov process , computer science , time sequence , algorithm , discrete mathematics , markov model , variable order markov model , statistics , biology , operating system , paleontology , genetics
Consider a discrete‐time regenerative phenomenon with associated renewal sequence u n . General results for the supremum of u m +1 , …, u m + n are developed for those renewal sequences { u n } for which the first m + 1 elements match those of a fixed renewal sequence { v n }, that is, u 0 = v 0 , …, u m = v m . A series of associated lemmas are developed in the process.