## The evolution of aggregated Markov chains

Autor(en): | Stadje, W |

Stichwörter: | aggregated Markov chain; conditional probability; Mathematics; MODELS; prediction; stationary sequence; Statistics & Probability; WEAK LUMPABILITY |

Erscheinungsdatum: | 2005 |

Herausgeber: | ELSEVIER SCIENCE BV |

Journal: | STATISTICS & PROBABILITY LETTERS |

Volumen: | 74 |

Ausgabe: | 4 |

Startseite: | 303 |

Seitenende: | 311 |

Zusammenfassung: | For a stationary two-sided Markov chain (X-n)(n is an element of Z) with finite state-space I and a partition I = Uv=0s-1Iv we consider the aggregated sequence defined by Y-n = v if X-n is an element of I-v, which is also stationary but in general not Markovian. We present a tractable way to determine the transition probabilities of either given a finite part of its past or given its infinite past. These probabilities are linked to the Radon-Nikodym derivative of P-Un vertical bar X-n=i with respect to P-Un, where U-n = Sigma(infinity)(m=1)s(-m)Y(n-m). (c) 2005 Elsevier B.V. All rights reserved. |

ISSN: | 01677152 |

DOI: | 10.1016/j.spl.2005.04.052 |

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