### Abstract

Language | English |
---|---|

Pages | 355002-355002 |

Number of pages | 0 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 41 |

Issue number | 35 |

DOIs | |

Publication status | Published - 5 Sep 2008 |

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### Keywords

- quantum optics
- hidden stochastic process

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*41*(35), 355002-355002. https://doi.org/10.1088/1751-8113/41/35/355002

}

*Journal of Physics A: Mathematical and Theoretical*, vol. 41, no. 35, pp. 355002-355002. https://doi.org/10.1088/1751-8113/41/35/355002

**The evolution of a single-paired immigration death process.** / Gillespie, C.S.; Renshaw, E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The evolution of a single-paired immigration death process

AU - Gillespie, C.S.

AU - Renshaw, E.

PY - 2008/9/5

Y1 - 2008/9/5

N2 - 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.

AB - 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.

KW - quantum optics

KW - hidden stochastic process

UR - http://dx.doi.org/10.1088/1751-8113/41/35/355002

U2 - 10.1088/1751-8113/41/35/355002

DO - 10.1088/1751-8113/41/35/355002

M3 - Article

VL - 41

SP - 355002

EP - 355002

JO - Journal of Physics A: Mathematical and Theoretical

T2 - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 0305-4470

IS - 35

ER -