Stability of Nonlinear Stochastic Volterra Difference Equations with Respect to a Fading Perturbation
Stability of Nonlinear Stochastic Volterra Difference Equations with Respect to a Fading Perturbation
复制标题
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
J. Appleby;A. Rodkina
中科院分区：
文献类型：
--
作者：
J. Appleby;A. Rodkina
研究了一类非线性沃尔泰拉差分方程在随机状态无关扰动下平衡解的随机稳定性和随机渐近稳定性。证明了如果线性化的确定性方程有可和解，则在初始条件和随机扰动强度足够小的条件下，非线性随机方程将是稳定的或渐近稳定的.强度的小密切遵循随机扰动线性沃尔泰拉差分方程的稳定性所需的条件。
The paper concerns studies the stochastic stability and stochastic asymptotic stability of the equilibrium solution of a nonlinear Volterra difference equation which is subject to stochastic state independent disturbances. It is shown that if the linearized deterministic equation has summable solutions, then the nonlinear stochastic equation will be stable or asymptotically stable, provided that the initial condition, and the intensity of the stochastic disturbances are sufficiently small. The smallness of the intensity follows closely the conditions required for the stability of the stochastically perturbed linear Volterra difference equation.