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Rare-event Simulation with Markov Chain Monte Carlo
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2013 (English)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesisAlternative title
Simulering av ovanligahändelser med MCMC (Swedish)
Abstract [en]

In this thesis, we consider random sums with heavy-tailed increments. By the term random sum, we mean a sum of random variables where the number of summands is also random. Our interest is to analyse the tail behaviour of random sums and to construct an efficient method to calculate quantiles. For the sake of efficiency, we simulate rare-events (tail-events) using a Markov chain Monte Carlo (MCMC) method. The asymptotic behaviour of sum and the maximum of heavy-tailed random sums is identical. Therefore we compare random sum and maximum value for various distributions, to investigate from which point one can use the asymptotic approximation. Furthermore, we propose a new method to estimate quantiles and the estimator is shown to be efficient.

Place, publisher, year, edition, pages
2013. , 35 p.
Trita-MAT-E, 2013:59
National Category
Mathematical Analysis
URN: urn:nbn:se:kth:diva-138950OAI: diva2:681969
Subject / course
Mathematical Statistics
Educational program
Master of Science in Engineering -Engineering Physics
Available from: 2013-12-20 Created: 2013-12-20 Last updated: 2013-12-20Bibliographically approved

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