## Abstract and Applied Analysis

### Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps

#### Abstract

We investigate a class of stochastic pantograph differential equations with Markovian switching and Levy jumps. We prove that the approximate solutions converge to the true solutions in ${L}^{2}$ sense as well as in probability under local Lipschitz condition and generalize the results obtained by Fan et al. (2007), Milošević and Jovanović (2011), and Marion et al. (2002) to cover a class of more general stochastic pantograph differential equations with jumps. Finally, an illustrative example is given to demonstrate our established theory.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 718627, 15 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511933

Digital Object Identifier
doi:10.1155/2013/718627

Mathematical Reviews number (MathSciNet)
MR3066295

Zentralblatt MATH identifier
07095276

#### Citation

Mao, Wei; Mao, Xuerong. Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps. Abstr. Appl. Anal. 2013 (2013), Article ID 718627, 15 pages. doi:10.1155/2013/718627. https://projecteuclid.org/euclid.aaa/1393511933

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