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

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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:	Date Event October 2014 Submitted
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Publication Status:	Unpublished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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