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The asymptotically mean square stability of the linear stochastic pantograph equation. (English) Zbl 1141.60350

Summary: The aim of this paper is to investigate the asymptotical mean square stability (MS-stable) of the analytical solution and the numerical method (the continuous \(\theta\)-method) for a linear stochastic pantograph equation. Conditions MS-stability of analytical solution and the numerical method are obtained.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65L20 Stability and convergence of numerical methods for ordinary differential equations
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