CONTENTS 0. Introduction...................................................................................5 0.1. Notations and preliminary results..............................................7 Chapter 1. Jump processes with drift.................................................9 1.1. Definition basic properties........................................................9 1.2. Characteristics of j.p.d............................................................12 1.2.1. Drift functions.....................................................................12 1.2.2. Drift time distributions.........................................................15 1.2.3. Jump distributions...............................................................15 1.2.4. Jump times, regeneration functions....................................18 1.2.5. Summary.............................................................................20 1.2.6. Characteristics and transition probabilities.........................21 1.3. Construction of j.p.d................................................................22 1.3.1. Construction of the "embedded chain"................................22 1.3.2. Construction of the j.p.d......................................................24 1.3.3. Characterization of j.p.d.......................................................29 Chapter 2. Feller j.p.d. on the real line..............................................29 2.1. Preparations.............................................................................30 2.2. Certain one-dimensional j.p.d....................................................33 2.2.1. Definition.............................................................................33 2.2.2. Existence of special Feller j.p.d...........................................34 2.3. Remarks. Discussion of results.................................................46 References........................................................................................50
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