A structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems

2012 ◽  
Vol 62 (7) ◽  
pp. 842-859 ◽  
Author(s):  
Evelyn Buckwar ◽  
Thorsten Sickenberger
Keyword(s):  
Structural Analysis ◽  
Mean Square ◽  
Differential Systems ◽  
Mean Square Stability

scholarly journals Mean Square Stability of Impulsive Stochastic Differential Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Shujie Yang ◽  
Bao Shi ◽  
Mo Li
Keyword(s):  
Stochastic Analysis ◽  
Functional Method ◽  
Stochastic Equations ◽  
Mean Square ◽  
Differential Systems ◽  
Numerical Examples ◽  
Mean Square Stability ◽  
Analysis Theory ◽  
Delay Dependent ◽  
Theoretical Results

Based on Lyapunov-Krasovskii functional method and stochastic analysis theory, we obtain some new delay-dependent criteria ensuring mean square stability of a class of impulsive stochastic equations. Numerical examples are given to illustrate the effectiveness of the theoretical results.

scholarly journals Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations

2003 ◽  
Vol 6 ◽  
pp. 297-313 ◽  
Author(s):  
Desmond J. Higham ◽  
Xuerong Mao ◽  
Andrew M. Stuart
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Finite Time ◽  
Mean Square ◽  
Convergence Conditions ◽  
Finite Time Convergence ◽  
Mean Square Stability ◽  
Exponential Mean Square Stability ◽  
Positive Results

AbstractPositive results are proved here about the ability of numerical simulations to reproduce the exponential mean-square stability of stochastic differential equations (SDEs). The first set of results applies under finite-time convergence conditions on the numerical method. Under these conditions, the exponential mean-square stability of the SDE and that of the method (for sufficiently small step sizes) are shown to be equivalent, and the corresponding second-moment Lyapunov exponent bounds can be taken to be arbitrarily close. The required finite-time convergence conditions hold for the class of stochastic theta methods on globally Lipschitz problems. It is then shown that exponential mean-square stability for non-globally Lipschitz SDEs is not inherited, in general, by numerical methods. However, for a class of SDEs that satisfy a one-sided Lipschitz condition, positive results are obtained for two implicit methods. These results highlight the fact that for long-time simulation on nonlinear SDEs, the choice of numerical method can be crucial.

Asymptotic mean-square stability of linear multi-step methods for SODEs

PAMM ◽  
2006 ◽  
Vol 6 (1) ◽  
pp. 659-660
Author(s):  
Evelyn Buckwar ◽  
Renate Winkler
Keyword(s):  
Mean Square ◽  
Mean Square Stability ◽  
Multi Step Methods
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