Asymptotic mean-square stability of weak second-order balanced stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential systems

2018 ◽  
Vol 332 ◽  
pp. 276-303
Author(s):  
Anandaraman Rathinasamy ◽  
Priya Nair
Keyword(s):  
Second Order ◽  
Mean Square ◽  
Differential Systems ◽  
Mean Square Stability ◽  
Runge Kutta

scholarly journals Mean-square stability of a class of stochastic integral equations

1972 ◽  
Vol 7 (3) ◽  
pp. 337-352
Author(s):  
W.J. Padgett
Keyword(s):  
Stochastic Process ◽  
Integral Equations ◽  
Stochastic Integral ◽  
Second Order ◽  
Mean Square ◽  
Random Solution ◽  
Mean Square Stability ◽  
Stochastic Integral Equations ◽  
Exponentially Stable ◽  
Image Position

The object of this paper is to investigate under very general conditions the existence and mean-square stability of a random solution of a class of stochastic integral equations in the formfor t ≥ 0, where a random solution is a second order stochastic process {x(t; w) t ≥ 0} which satisfies the equation almost certainly. A random solution x(t; w) is defined to be stable in mean-square if E[|x(t; w)|2] ≤ p for all t ≥ 0 and some p > 0 or exponentially stable in mean-square if E[|x(t; w)|2] ≤ pe-at, t ≥ 0, for some constants ρ > 0 and α > 0.

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.

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