Stochastic Theta Method for a Reflected Stochastic Differential Equation

In this article, a stochastic theta method for a reflected stochastic differential equation is proposed. When the parameter θ = 0, this method coincides with the projection Euler scheme; while when the parameter θ = 1, it is called an implicit projection Euler scheme which is first proposed in this...

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Bibliographic Details
Published inNumerical functional analysis and optimization Vol. 35; no. 6; pp. 752 - 776
Main Author Zhang, Haisen
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 03.06.2014
Subjects
A-stable
Convergence
Differential equations
Functional analysis
Mathematical models
Optimization
Projection
Reflected stochastic differential equation
Skorokhod problem
Stochastic theta method
Stochasticity
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Summary:In this article, a stochastic theta method for a reflected stochastic differential equation is proposed. When the parameter θ = 0, this method coincides with the projection Euler scheme; while when the parameter θ = 1, it is called an implicit projection Euler scheme which is first proposed in this article. Under some conditions, the strong convergence and the A-stability of this numerical scheme are proved.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2013.837068