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....
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/718627 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832568307191906304 |
|---|---|
| author | Wei Mao Xuerong Mao |
| author_facet | Wei Mao Xuerong Mao |
| author_sort | Wei Mao |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-a07905a4552944d898262a2158977397 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a07905a4552944d898262a21589773972025-02-03T00:59:19ZengWileyAbstract 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 |
| spellingShingle | Wei Mao Xuerong Mao Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps Abstract and Applied Analysis |
| title | 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_short | Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps |
| title_sort | approximate solutions of hybrid stochastic pantograph equations with levy jumps |
| url | http://dx.doi.org/10.1155/2013/718627 |
| work_keys_str_mv | AT weimao approximatesolutionsofhybridstochasticpantographequationswithlevyjumps AT xuerongmao approximatesolutionsofhybridstochasticpantographequationswithlevyjumps |