  In this paper, we study the polynomial stability of analytical solution and
convergence of the semi-implicit Euler method for non-linear stochastic
pantograph differential equations. Firstly, the sufficient conditions for
solutions to grow at a polynomial rate in the sense of mean-square and almost
surely are obtained. Secondly, the consistence and convergence of this method
are proved. Furthermore, the orders of consistence (in the sense of average and
mean-square) and convergence are given, respectively.
