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Stochastic Differential Equations: and the numerical schemes used to solve them
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

This thesis explains the theoretical background of stochastic differential equations in one dimension. We also show how to solve such differential equations using strong It o-Taylor expansion schemes over large time grids. We also attempt to solve a problem regarding a specific approximation of a stochastic integral for which there is no explicit solution. This approximation, which utilizes the distribution of this particular stochastic integral, gives the wrong order of convergence when performing a grid convergence study. We use numerical integration of the stochastic integral as an alternative approximation, which is correct with regards to convergence.

Place, publisher, year, edition, pages
2014. , 44 p.
Keyword [en]
stochastic differential equations, o-Taylor expansion schemes
National Category
Probability Theory and Statistics
URN: urn:nbn:se:umu:diva-86799OAI: diva2:704100
Available from: 2014-03-26 Created: 2014-03-11 Last updated: 2014-03-26Bibliographically approved

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