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Zbl 1225.60120
Yu, Zhanhua
Almost surely asymptotic stability of exact and numerical solutions for neutral stochastic pantograph equations. (English)
[J] Abstr. Appl. Anal. 2011, Article ID 143079, 14 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

Summary: 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 2000:
*60H35 Computational methods for stochastic equations
93E15 Stochastic stability

Keywords: neutral stochastic pantograph equations; asymptotic stability

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