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Title: N-dimension numerical solution of stochastic differential equations
Author: Li, Qiming
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2007
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We introduce an order γ(γ>1/2) strong scheme and an improved weak scheme for the numerical approximation of solutions to stochastic differential equations (SDEs), driven by N Weinner processes. The strong scheme, called the ¾ Scheme, which is dependent on a differently constructed Brownian path, involves the area terms to bring better asymptotic accuracy than any numerical method based on classic constructed N-Dimension Brownian path. We demonstrate how to construct such a Brownian path, besides how to subdivide the Brownian path to get a sequence of approximations which converges pathwise as h tends to 0. We prove that the convergence of such method is guaranteed if the time step size h tends to 0. We also present the Improved Weak Euler Scheme (IWES), whose sample error is much smaller than the classic Weak Euler Scheme’s. The method reduces computation load and the sample error, which is generated during the Monte-Carlo(MC) approximation, by balancing the times of Euler iteration and MC simulation. A further improved IWES can be achieved by reusing the Brownian path. We prove that the extra sample error from reusing Brownian path is negligible in the latter method.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available