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Markov chain approximations to scale functions of Lévy processes
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Mijatović, Aleksandar, Vidmar, Matija and Jacka, Saul D. (2015) Markov chain approximations to scale functions of Lévy processes. Stochastic Processes and their Applications, 125 (10). pp. 3932-3957. doi:10.1016/j.spa.2015.05.012
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WRAP_8473264-st-060116-scale_functions-short.pdf - Accepted Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. Download (1400Kb) | Preview |
Official URL: http://dx.doi.org/10.1016/j.spa.2015.05.012
Abstract
We introduce a general algorithm for the computation of the scale functions of a spectrally negative Lévy process X, based on a natural weak approximation of X via upwards skip-free continuous-time Markov chains with stationary independent increments. The algorithm consists of evaluating a finite linear recursion with its (nonnegative) coefficients given explicitly in terms of the Lévy triplet of X. Thus it is easy to implement and numerically stable. Our main result establishes sharp rates of convergence of this algorithm providing an explicit link between the semimartingale characteristics of X and its scale functions, not unlike the one-dimensional Itô diffusion setting, where scale functions are expressed in terms of certain integrals of the coefficients of the governing SDE.
| Item Type: | Journal Article | ||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||
| Divisions: | Faculty of Science > Statistics | ||||||||||
| Library of Congress Subject Headings (LCSH): | Markov processes, Lévy processes, Brownian motion processes, Semimartingales (Mathematics) | ||||||||||
| Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||||
| Publisher: | Elsevier Science BV | ||||||||||
| ISSN: | 0304-4149 | ||||||||||
| Official Date: | October 2015 | ||||||||||
| Dates: |
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| Date of first compliant deposit: | 14 January 2016 | ||||||||||
| Volume: | 125 | ||||||||||
| Number: | 10 | ||||||||||
| Page Range: | pp. 3932-3957 | ||||||||||
| DOI: | 10.1016/j.spa.2015.05.012 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Restricted or Subscription Access |
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