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Multi-scale methods for stochastic differential equations
Umeå University, Faculty of Science and Technology, Department of Physics.
2012 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Flerskaliga metoder för stockastiska differentialekvationer (Swedish)
Abstract [en]

Standard Monte Carlo methods are used extensively to solve stochastic differential equations. This thesis investigates a Monte Carlo (MC) method called multilevel Monte Carlo that solves the equations on several grids, each with a specific number of grid points. The multilevel MC reduces the computational cost compared to standard MC. When using a fixed computational cost the variance can be reduced by using the multilevel method compared to the standard one. Discretization and statistical error calculations are also being conducted and the possibility to evaluate the errors coupled with the multilevel MC creates a powerful numerical tool for calculating equations numerically. By using the multilevel MC method together with the error calculations it is possible to efficiently determine how to spend an extended computational budget.

Abstract [sv]

Standard Monte Carlo metoder används flitigt för att lösa stokastiska differentialekvationer. Denna avhandling undersöker en Monte Carlo-metod (MC) kallad multilevel Monte Carlo som löser ekvationerna på flera olika rutsystem, var och en med ett specifikt antal punkter. Multilevel MC reducerar beräkningskomplexiteten jämfört med standard MC. För en fixerad beräkningskoplexitet kan variansen reduceras genom att multilevel MC-metoden används istället för standard MC-metoden. Diskretiserings- och statistiska felberäkningar görs också och möjligheten att evaluera de olika felen, kopplat med multilevel MC-metoden skapar ett kraftfullt verktyg för numerisk beräkning utav ekvationer. Genom att använda multilevel MC tillsammans med felberäkningar så är det möjligt att bestämma hur en utökad beräkningsbudget speneras så effektivt som möjligt.

Place, publisher, year, edition, pages
2012. , 47 p.
Keyword [en]
multilevel, Monte Carlo, multi-scale, stochastic differential equations
National Category
Probability Theory and Statistics
URN: urn:nbn:se:umu:diva-53704OAI: diva2:513927
Subject / course
Examensarbete i teknisk fysik
Educational program
Civilingenjörsprogrammet i teknisk fysik
2012-03-30, Universitetsklubben, Universumhuset, våning 3, Umeå, 14:00 (Swedish)
Physics, Chemistry, Mathematics
Available from: 2012-04-04 Created: 2012-04-04 Last updated: 2012-04-04Bibliographically approved

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Zettervall, Niklas
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