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008 210411s2020 ua d f m 000 0 eng d
040 _aEG-GiCUC
_beng
_cEG-GiCUC
041 0 _aeng
049 _aDeposite
097 _aM.Sc
099 _aCai01.13.10.M.Sc.2020.Sh.M
100 0 _aShady Ahmed Nagy
245 1 0 _aMultilevel monte carlo methods for solution of stochastic differential equations and its applications /
_cShady Ahmed Nagy ; Supervised Mohamed A. Elbeltagy , Mohamed Wafa
246 1 5 _aطرق مونت كارلو متعددة المستويات لحل المعادلات التفاضلية العشوائية وتطبيقاتها
260 _aCairo :
_bShady Ahmed Nagy ,
_c2020
300 _a112 P. :
_bcharts , facimiles ;
_c30cm
502 _aThesis (M.Sc.) - Cairo University - Faculty of Engineering - Department of Mathematics and Physics
520 _aMonte Carlo simulation is wide using in solving stochastic differential equations. Stochastic random samples represent by different random points in Monte Carlo random generation. The development of Multilevel Monte Carlo (MLMC) introduced by Giles to simulate different stochastic differential equations on different time grids by low cost and high convergence rate, also it minimizes the variance. We simulate and compare different type of stochastic differential equations on MLMC depending on Quasi-Monte Carlo of Halton sequence. We apply MLMC in diffrent types of ordinary SDEs as additive and multiplicative one to enhance cost by changing the random sample to be generated by different quasi-random numbers. Also, we use a different type of quasi-random numbers by Component by Component (CBC) algorithm that generates different random numbers by the concept of lattice rule. When we apply it in stochastic Burgers{u2019} equations, theinstability appears in simulation by doesn{u2019}t achieve the decreasing in cost despite the minimum time of CBC numbers that generate the stochastic samples
530 _aIssued also as CD
653 4 _aNumerical analysis
653 4 _aStochastic differential equations
653 4 _aStochastic processes
700 0 _aMohamed A. Elbeltagy ,
_eSupervisor
700 0 _aMohamed Wafa ,
_eSupervisor
856 _uhttp://172.23.153.220/th.pdf
905 _aNazla
_eRevisor
905 _aShimaa
_eCataloger
942 _2ddc
_cTH
999 _c80618
_d80618