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long rangebernard brurange dependencedependence selfself similarityconversation bernardbrownian motiontime series analysisbachelier timestimes conversationrange dependentfractional brownianlouis bachelierstock exchangeestimation theorynoise tradingstochastischer prozessstochastic processportfolio managementportfolio selectionsimilarity asymptoticasymptotic codifferencecodifference covariationcovariation loglog fractionalfractional stablestable noisenoise multimulti selfself similarsimilar randomrandom fieldsfields multivariatemultivariate lampertilamperti transformationtransformation testingtesting diffusiondiffusion processesprocesses nonnon stationaritystationarity estimatorsestimators longlong memorymemory fourierfourier versusversus waveletswavelets extremeextreme valuevalue approachapproach allocationallocation multiplemultiple assetsassets financialfinancial riskrisk heavyheavy tailstails bachelierbru bachelierbru optionoption pricingpricing archarch typetype models
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