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Abstract and Applied Analysis
Volume 2013, Article ID 420648, 10 pages
http://dx.doi.org/10.1155/2013/420648
Research Article

Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps

1College of Electrical and Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China
2Jiangsu Meteorological Observatory, Nanjing 210008, China
3College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China

Received 8 April 2013; Accepted 5 June 2013

Academic Editor: Zidong Wang

Copyright © 2013 Zhenyu Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The sufficient conditions of existence and uniqueness of the solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps are given. It is proved that Euler-Maruyama scheme for nonlinear stochastic pantograph equations with Markovian switching and Brownian motion is of convergence with strong order 1/2. For nonlinear stochastic pantograph equations with Markovian switching and pure jumps, it is best to use the mean-square convergence, and the order of mean-square convergence is close to 1/2.