Christian Lècot (Laboratoire de Mathèmatiques, Universitè Savoie Mont Blanc)

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Christian Lècot (Laboratoire de Mathèmatiques, Universitè Savoie Mont Blanc)

June 8, 2016 @ 4:00 pm - 5:00 pm UTC+0

Quasi-Monte Carlo Methods for Estimating Transient Measures of Discrete Time Markov Chains

Markov 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.

On 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.

In 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.

During 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.


June 8, 2016
4:00 pm - 5:00 pm UTC+0
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Room 205
2-5, Kirkby Place
Plymouth, PL4 6DT United Kingdom
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