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Markov chain approximations to, and some fluctuation results for, Lévy processes

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Vidmar, Matija (2014) Markov chain approximations to, and some fluctuation results for, Lévy processes. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b2749483~S1

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Abstract

We introduce, and analyze in terms of convergence rates of transition kernels, a continuous-time Markov chain approximation to Lévy processes. A full fluctuation theory for what are right-continuous random walks embedded into continuous-time as compound Poisson processes, is provided. These results are applied to obtaining a general algorithm for the calculation of the scale functions of a spectrally negative Lévy process. In a related result, the class of Lévy processes having non-random overshoots is precisely characterized.

Item Type: Thesis (PhD)
Subjects: Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH): Lévy processes, Markov processes
Official Date: October 2014
Dates:
DateEvent
October 2014Submitted
Institution: University of Warwick
Theses Department: Department of Statistics
Thesis Type: PhD
Publication Status: Unpublished
Supervisor(s)/Advisor: Mijatović, Aleksandar ; Jacka, Saul D.
Sponsors: Javni Sklad Republike Slovenije za Razvoj Kadrov in Štipendije [Slovene Human Resources and Scholarship Fund] (11010-543/2011)
Extent: v, 129 leaves
Language: eng

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