![](/images/graphics-bg.png)
Mean-Square Stability of Split-Step Theta Milstein Methods for Stochastic Differential Equations
Joint Authors
Xiao, Yu
Eissa, Mahmoud A.
Zhang, Haiying
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-01-24
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The fundamental analysis of numerical methods for stochastic differential equations (SDEs) has been improved by constructing new split-step numerical methods.
In this paper, we are interested in studying the mean-square (MS) stability of the new general drifting split-step theta Milstein (DSSθM) methods for SDEs.
First, we consider scalar linear SDEs.
The stability function of the DSSθM methods is investigated.
Furthermore, the stability regions of the DSSθM methods are compared with those of test equation, and it is proved that the methods with θ≥3/2 are stochastically A-stable.
Second, the nonlinear stability of DSSθM methods is studied.
Under a coupled condition on the drifting and diffusion coefficients, it is proved that the methods with θ>1/2 can preserve the MS stability of the SDEs with no restriction on the step-size.
Finally, numerical examples are given to examine the accuracy of the proposed methods under the stability conditions in approximation of SDEs.
American Psychological Association (APA)
Eissa, Mahmoud A.& Zhang, Haiying& Xiao, Yu. 2018. Mean-Square Stability of Split-Step Theta Milstein Methods for Stochastic Differential Equations. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1205753
Modern Language Association (MLA)
Eissa, Mahmoud A.…[et al.]. Mean-Square Stability of Split-Step Theta Milstein Methods for Stochastic Differential Equations. Mathematical Problems in Engineering No. 2018 (2018), pp.1-13.
https://search.emarefa.net/detail/BIM-1205753
American Medical Association (AMA)
Eissa, Mahmoud A.& Zhang, Haiying& Xiao, Yu. Mean-Square Stability of Split-Step Theta Milstein Methods for Stochastic Differential Equations. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1205753
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1205753