The evolution of a single-paired immigration death process

C.S. Gillespie, E. Renshaw

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The general question of whether it is possible to determine the fundamental structure of a hidden stochastic process purely from counts of escaping individuals is of immense importance in fields such as quantum optics, where externally based radiation elucidates the nature of the electromagnetic radiation process. Although the general probability structure has been derived in an earlier paper in terms of the joint probability generating function of the (hidden) population size and (known) counts, its complex nature hides some particularly intriguing features of the underlying process. Our current objective is therefore to examine specific immigration regimes in order to highlight the underlying saw-tooth behaviour of the underlying probability and moment structures. The paper first explores paired- and triple-immigration schemes, and then introduces birth in order to showthat the technique is equally successful in exposing hidden multiplicative effects. These analyses uncover novel and highly illuminating features, and emphasize the potential of this population-counting construct for expanding into more complex multi-type situations.
Original languageEnglish
Pages (from-to)355002-355002
Number of pages0
JournalJournal of Physics A: Mathematical and Theoretical
Volume41
Issue number35
DOIs
Publication statusPublished - 5 Sep 2008

Keywords

  • quantum optics
  • hidden stochastic process

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