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DTSTART:20160101T000000
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DTSTART;TZID=UTC:20160608T160000
DTEND;TZID=UTC:20160608T170000
DTSTAMP:20211023T182755
CREATED:20160518T092304Z
LAST-MODIFIED:20160522T120927Z
UID:1651-1465401600-1465405200@math-sciences.org
SUMMARY:Christian Lècot (Laboratoire de Mathèmatiques\, Universitè Savoie Mont Blanc)
DESCRIPTION:Quasi-Monte Carlo Methods for Estimating Transient Measures of Discrete Time Markov Chains \n\n\n\n\nMarkov chains are probably the most widely used type of models in fields such as physics\, queueing or reliability theory\, telecommunications\, etc. In many situations\, the state space that has to be dealt with is so large that an- alytical methods are intractable to solve the models\, due to both the compu- tational time and the memory requirements. Then the only valuable method is Monte Carlo simulation. \nOn another hand\, quasi-Monte Carlo (QMC) methods are known to out- perform Monte Carlo (MC) methods in terms of convergence speed in many situations. Instead of pseudo-random numbers in MC\, low discrepancy se- quences are used to benefit from their repartition over the integration space. \nIn this presentation\, we deal with the transient QMC simulation of dis- crete time Markov chains. We propose to use a QMC method where different paths are simulated in parallel\, but relabeled at each step. This way\, the es- timation converges to the true value\, and only a low discrepancy sequence in low dimension is required. \nDuring the presentation\, we initially describe the method for Markov chains with one-dimensional discrete state spaces; we prove its convergence\, as the number of simulated paths increases. The method is generalized to the cases of multidimensional\, discrete or continuous state spaces; it is ex- tended to randomized QMC approaches; its validity is illustrated on various examples.
URL:http://math-sciences.org/event/christian-lecot-laboratoire-de-mathematiques-universite-savoie-mont-blanc/
LOCATION:Room 205\, 2-5\, Kirkby Place\, Plymouth\, PL4 6DT\, United Kingdom
CATEGORIES:Applied Mathematics,Seminars
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