## Abstract

In Markov chain models, given an empirically observed transition matrix over a certain time interval, it may be needed to extract information about the transition probabilities over some shorter time interval. This is called an embedding problem. In a discrete time setting this problem comes down to finding a transition matrix Q which is a stochastic p-th root (p is an integer) of a given transition matrix P. It is known that an embedding problem need not have a unique solution, so the question arises as to identify those solutions that can be retained for further modelling purposes. In manpower planning applications, it is reasonable to assume that promotion prospects decrease over shorter periods of time. Therefore, we focus on transition matrices Q which have off-diagonal elements that are not exceeding the corresponding elements of P and call those matrices

stepwise increasing. In this paper, we present some results about stepwise increasing stochastic square roots (p = 2) of a given transition matrix for the two- and three-state case.

stepwise increasing. In this paper, we present some results about stepwise increasing stochastic square roots (p = 2) of a given transition matrix for the two- and three-state case.

Original language | English |
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Title of host publication | SMTDA2016 Book of abstracts 4th Stochastic Modeling Techniques & Data Analysis International Conference |

Editors | Christos H. Skiadas |

Publisher | ISAST: International Society for the Advancement of Science and Technology. |

Pages | 22-22 |

Number of pages | 1 |

ISBN (Electronic) | 978-618-5180-15-7 |

ISBN (Print) | 978-618-5180-14-0 |

Publication status | Published - 2016 |

Event | Stochastic Modeling Techniques and Data Analysis International Conference - University of Malta, Valetta, Malta Duration: 1 Jun 2016 → 4 Jun 2016 http://www.smtda.net/ http://www.smtda.net/ |

### Conference

Conference | Stochastic Modeling Techniques and Data Analysis International Conference |
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Abbreviated title | SMTDA2016 |

Country/Territory | Malta |

City | Valetta |

Period | 1/06/16 → 4/06/16 |

Internet address |

## Keywords

- Markov chain models