Almost surely asymptotic stability of exact and numerical solutions for neutral stochastic pantograph equations.

*(English)*Zbl 1225.60120Summary: We study the almost sure asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs), and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM) with variable stepsize can preserve the almost sure asymptotic stability. Numerical examples are presented for illustration.

##### MSC:

60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |

93E15 | Stochastic stability in control theory |

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\textit{Z. Yu}, Abstr. Appl. Anal. 2011, Article ID 143079, 14 p. (2011; Zbl 1225.60120)

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