A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations
It is well known that Itô’s formula is an essential tool in stochastic analysis. But it cannot be used for general stochastic Volterra integral equations (SVIEs). In this paper, we first introduce the concept of quasi-Itô process which is a generalization of well-known Itô process. And then we exten...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/292740 |
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| _version_ | 1832560897645608960 |
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| author | Wenxue Li Meng Liu Ke Wang |
| author_facet | Wenxue Li Meng Liu Ke Wang |
| author_sort | Wenxue Li |
| collection | DOAJ |
| description | It is well known that Itô’s formula is an essential tool in stochastic analysis. But it cannot be used for general stochastic Volterra integral equations (SVIEs). In this paper, we first introduce the concept of quasi-Itô process which is a generalization of well-known Itô process. And then we extend Itô’s formula to a more general form applicable to some kinds of SVIEs. Furthermore, the stability in probability for some SVIEs is analyzed by the generalized Itô’s formula. Our work shows that the generalized Itô’s formula is powerful and flexible to use in many relevant fields. |
| format | Article |
| id | doaj-art-ba95b1744cf34ae7a54fd874c9d4f7c9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ba95b1744cf34ae7a54fd874c9d4f7c92025-02-03T01:26:32ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/292740292740A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral EquationsWenxue Li0Meng Liu1Ke Wang2Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, ChinaIt is well known that Itô’s formula is an essential tool in stochastic analysis. But it cannot be used for general stochastic Volterra integral equations (SVIEs). In this paper, we first introduce the concept of quasi-Itô process which is a generalization of well-known Itô process. And then we extend Itô’s formula to a more general form applicable to some kinds of SVIEs. Furthermore, the stability in probability for some SVIEs is analyzed by the generalized Itô’s formula. Our work shows that the generalized Itô’s formula is powerful and flexible to use in many relevant fields.http://dx.doi.org/10.1155/2012/292740 |
| spellingShingle | Wenxue Li Meng Liu Ke Wang A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations Journal of Applied Mathematics |
| title | A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations |
| title_full | A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations |
| title_fullStr | A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations |
| title_full_unstemmed | A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations |
| title_short | A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations |
| title_sort | generalization of ito s formula and the stability of stochastic volterra integral equations |
| url | http://dx.doi.org/10.1155/2012/292740 |
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