《Randomized Dimension Reduction for Monte Carlo Simulations蒙特卡洛模擬的隨機(jī)化降維》由會員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫。

1、RandomizedDimensionReductionforMonteCarloSimulationsNabilKahal′e?December14,2017AbstractWepresentanewunbiasedalgorithmthatestimatestheexpectedvalueoff(U)viaMonteCarlosimulation,whereUisavectorofdindependentrandomvariables,andfisafunctionofdvariables.Weassumethatfdoesnotdependequallyonallitsarg

2、uments.Undercertainconditionsweprovethat,forthesamecomputationalcost,thevarianceofourestimatorislowerthanthevarianceofthestandardMonteCarloestimatorbyafactoroforderd.Ourmethodcanbeusedtoobtainalow-varianceunbiasedestimatorfortheexpectationofafunctionofthestateofaMarkovchainatagiventime-step.We

3、studyapplicationstovolatilityforecastingandtime-varyingqueues.NumericalexperimentsshowthatouralgorithmdramaticallyimprovesuponthestandardMonteCarlomethodforlargevaluesofd,andishighlyresilienttodiscontinuities.Keywords:dimensionreduction;variancereduction;e?ectivedimension;Markovchains;MonteCar

4、lomethods1IntroductionMarkovchainsariseinavarietyof?eldssuchas?nance,queuingtheory,andsocialnetworks.Whilemuchresearchhasbeendevotedtothestudyofsteady-statesofMarkovchains,sev-eralpracticalapplicationsrelyonthetransientbehaviorofMarkovchains.Forexample,thevolatilityofanindexcanbemodelledasaMar

5、kovchainusingtheGARCHmodel(Hull2014,Ch.23).Financialinstitutionsconductingstresstestsmayneedtoestimatetheprobabilitythatthevolatilityexceedsagivenlevelinafewyearsfromnow.Also,duetothenatureofhumanactivity,queuingsystemsinareassuchashealth-care,manufacturing,telecommunica-tionandtransportationn

6、etworks,haveoftentime-varyingfeaturesanddonothaveasteady-state.Forinstance,empiricaldatashowsigni?cantdailyvariationintra?cinwide-areanet-works(Paxson1994,Thompson,MillerandWilder1997)andvehicular?owonroads(Nagel,WagnerandWoesler2003).Estimatingtheexpecteddelayofpacketsinawide-areanetworkatarX

7、iv:1708.07466v2[stat.CO]13Dec2017aspeci?ctimeoftheday(12pm,say)couldbeusedtodimensionsuchnetworks.Similarly,esti-matingthevelocityofcarsinaregionat6pmcouldbeusedtodesigntransportationnetworks.Inthesamevein,considertheproblemofestimating