Bridges with Random Length: Gamma Case

Mohamed Erraoui (), Astrid Hilbert () and Mohammed Louriki ()
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Mohamed Erraoui: Université Cadi Ayyad
Astrid Hilbert: Linnaeus University
Mohammed Louriki: Université Cadi Ayyad

Journal of Theoretical Probability, 2020, vol. 33, issue 2, 931-953

Abstract: Abstract In this paper, we generalize the concept of gamma bridge in the sense that the length will be random, that is, the time to reach the given level is random. The main objective of this paper is to show that certain basic properties of gamma bridges with deterministic length stay true also for gamma bridges with random length. We show that the gamma bridge with random length is a pure jump process and that its jumping times are countable and dense in the random interval bounded by 0 and the random length. Moreover, we prove that this process is a Markov process with respect to its completed natural filtration as well as with respect to the usual augmentation of this filtration, which leads us to conclude that its completed natural filtration is right continuous. Finally, we give its canonical decomposition with respect to the usual augmentation of its natural filtration.

Keywords: Lévy processes; Gamma processes; Gamma bridges; Markov process; Bayes theorem; 60G40; 60G46; 60G51; 60H10; 60J75 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00955-4

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