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Multilevel monte carlo methods for solution of stochastic differential equations and its applications / Shady Ahmed Nagy ; Supervised Mohamed A. Elbeltagy , Mohamed Wafa

By: Contributor(s): Material type: TextTextLanguage: English Publication details: Cairo : Shady Ahmed Nagy , 2020Description: 112 P. : charts , facimiles ; 30cmOther title:
  • طرق مونت كارلو متعددة المستويات لحل المعادلات التفاضلية العشوائية وتطبيقاتها [Added title page title]
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Dissertation note: Thesis (M.Sc.) - Cairo University - Faculty of Engineering - Department of Mathematics and Physics Summary: Monte 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
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Thesis Thesis قاعة الرسائل الجامعية - الدور الاول المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.13.10.M.Sc.2020.Sh.M (Browse shelf(Opens below)) Not for loan 01010110083227000
CD - Rom CD - Rom مخـــزن الرســائل الجـــامعية - البدروم المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.13.10.M.Sc.2020.Sh.M (Browse shelf(Opens below)) 83227.CD Not for loan 01020110083227000

Thesis (M.Sc.) - Cairo University - Faculty of Engineering - Department of Mathematics and Physics

Monte 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

Issued also as CD

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