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## Markov Chains, Renewal, Branching and Coalescent Processes : Four Topics in Probability Theory

<p>This thesis consists of four papers.</p><p>In paper 1, we prove central limit theorems for Markov chains under (local) contraction conditions. As a corollary we obtain a central limit theorem for Markov chains associated with iterated function systems with contractive maps and place-dependent Dini-continuous probabilities.</p><p>In paper 2, properties of inverse subordinators are investigated, in particular similarities with renewal processes. The main tool is a theorem on processes that are both renewal and Cox processes.</p><p>In paper 3, distributional properties of supercritical and especially immortal branching processes are derived. The marginal distributions of immortal branching processes are found to be compound geometric.</p><p>In paper 4, a description of a dynamic population model is presented, such that samples from the population have genealogies as given by a Lambda-coalescent with mutations. Depending on whether the sample is grouped according to litters or families, the sampling distribution is either regenerative or non-regenerative.</p>

Identifer | oai:union.ndltd.org:UPSALLA/oai:DiVA.org:su-6637 |

Date | January 2007 |

Creators | Nordvall LagerÃ¥s, Andreas |

Publisher | Stockholm University, Department of Mathematics, Stockholm : Matematiska institutionen |

Source Sets | DiVA Archive at Upsalla University |

Language | English |

Detected Language | English |

Type | Doctoral thesis, comprehensive summary, text |

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