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Title: Markov chain approximations to, and some fluctuation results for, Lévy processes
Author: Vidmar, Matija
ISNI:       0000 0004 5357 3849
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2014
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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.
Supervisor: Not available Sponsor: Javni Sklad Republike Slovenije za Razvoj Kadrov in Štipendije (Slovene Human Resources and Scholarship Fund) (11010-543/2011)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics