Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps

Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps

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 sense as well as in probability under local Lipschitz condition and generalize the results obtained by Fan et al....

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Main Authors: Wei Mao, Xuerong Mao
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/718627
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spelling doaj-a07905a4552944d898262a21589773972020-11-24T22:34:39ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/718627718627Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy JumpsWei Mao0Xuerong Mao1School of Mathematics and Information Technology, Jiangsu Second Normal University, Nanjing 210013, ChinaDepartment of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, UKWe 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 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.http://dx.doi.org/10.1155/2013/718627
collection DOAJ
language English
format Article
sources DOAJ
author Wei Mao
Xuerong Mao
spellingShingle Wei Mao
Xuerong Mao
Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps
Abstract and Applied Analysis
author_facet Wei Mao
Xuerong Mao
author_sort Wei Mao
title Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps
title_short Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps
title_full Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps
title_fullStr Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps
title_full_unstemmed Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps
title_sort approximate solutions of hybrid stochastic pantograph equations with levy jumps
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description 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 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.
url http://dx.doi.org/10.1155/2013/718627
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AT xuerongmao approximatesolutionsofhybridstochasticpantographequationswithlevyjumps
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