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Rare events simulation by shaking transformations : Non-intrusive resampler for dynamic programming

Abstract : This thesis contains two parts: rare events simulation and non-intrusive stratified resampler for dynamic programming. The first part consists of quantifying statistics related to events which are unlikely to happen but which have serious consequences. We propose Markovian transformation on path spaces and combine them with the theories of interacting particle system and of Markov chain ergodicity to propose methods which apply very generally and have good performance. The second part consists of resolving dynamic programming problem numerically in a context where we only have historical observations of small size and we do not know the values of model parameters. We propose and analyze a new scheme with stratification and resampling techniques.
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Gang Liu. Rare events simulation by shaking transformations : Non-intrusive resampler for dynamic programming. Probability [math.PR]. Université Paris-Saclay, 2016. English. ⟨NNT : 2016SACLX043⟩. ⟨tel-01493795⟩

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