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UM E-Theses Collection (澳門大學電子學位論文庫)

Title

Numerical solutions for reflected stochastic differential equations in R+

English Abstract

In this thesis, we analyze Reflected Stochastic Differential Equation (RSDE) in the upper half space ℝ⁺. Various numerical schemes and methods for this kind of RSDE are surveyed, and exemplifed by numerical experiments based on MATLAB programs. The thesis is divided into four chapters. A brief introduction to SDE, two discretization numerical schemes: Euler scheme, Milstein scheme, and also a numerical example is given in Chapter 1. In Chapter 2, a brief introduction to RSDE in the upper half space ℝ⁺, and some different Euler-type schemes for RSDEs are given, with some numerical experiments. In Chapter 3, a new algorithm for RSDE based on the splitting-step idea and penalization method is presented. Its convergence result is reported, a numerical scheme based the suggested algorithm is also given, and some numerical experiments are given to support this algorithm. In Chapter 4,some Milstein-type schemes for RSDE (2.1.1) are presented, and numerical experiments for some RSDEs are done to compare the convergence rates of the corresponding Euler-type and Milstein-type schemes. These numerical experiments suggest that the presented Milstein-type schemes could not rise the convergence rate for numerical approximations for some RSDEs.

Issue date

2007.

Author

Zhang, Ying Ying,

Faculty

Faculty of Science and Technology

Department

Department of Mathematics

Degree

M.Sc.

Subject

Stochastic differential equations

Supervisor

Ding, Deng

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Location
1/F Zone C
Library URL
991000943439706306