Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1035.65009
Saito, Yoshihiro; Mitsui, Taketomo
Mean-square stability of numerical schemes for stochastic differential systems. (English)
[J] Vietnam J. Math. 30, Spec. Issue, 551-560 (2002). ISSN 2305-221X; ISSN 2305-2228/e

Criteria are derived for establishing mean-square (MS)-stability of the system of stochastic differential equations $$d{\bold X}(t)= {\bold D}{\bold X}(t)\,dt+{\bold B}{\bold X}(t)\,dW(t),\quad{\bold X}(0)= 1,$$ where $${\bold D}= \left[\matrix\lambda_1 & 0\\ 0 &\lambda_2\endmatrix\right],\qquad{\bold B}= \left[\matrix \alpha_1 &\beta_1\\ \beta_2 &\alpha_2\endmatrix\right],$$ and $W(t)$ is a Wiener process. This leads to criteria under which the Euler-Maruyama method for approximating the solution of the system will be numerically MS-stable, and to the identification of its region of MS-stability. Results of numerical experiments are presented which affirm the accuracy of the criteria.
[Melvin D. Lax (Long Beach)]

MSC 2000:: *65C30 Stochastic differential and integral equations
60H10 Stochastic ordinary differential equations
65L06 Multistep, Runge-Kutta, and extrapolation methods
65L20 Stability of numerical methods for ODE
60H35 Computational methods for stochastic equations

Keywords: system of stochastic differential equations; Euler-Maruyama method; numerical experiments; mean square stability

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]