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Existence and uniqueness of the solutions and convergence of semi-implicit Euler methods for stochastic pantograph equations
Authors:Zhencheng Fan  Mingzhu Liu  Wanrong Cao
Institution:Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China
Abstract:In this paper the sufficient conditions of existence and uniqueness of the solutions for stochastic pantograph equation are given, i.e., the local Lipschitz condition and the linear growth condition. Under the Lipschitz condition and the linear growth condition it is proved that the semi-implicit Euler method is convergence with strong order View the MathML source.
Keywords:Stochastic delay differential equation  Stochastic pantograph differential equation  Semi-implicit Euler method  The strong convergence
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