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http://dspace.univ-bouira.dz:8080/jspui/handle/123456789/10598| Title: | New inequalities of Gronwall type for the stochastic di erential equations |
| Authors: | Boudref, Mohamed Ahmed Berboucha, Ahmed |
| Keywords: | Stochastic di erential equation, Itô integral, Gronwall–Bellman inequality |
| Issue Date: | 14-Apr-2015 |
| Publisher: | DE GRUYTER |
| Abstract: | In this paper, we establish some new nonlinear integral inequalities of Gronwall type for Itô integrals. These inequalities generalize some inequalities which can be used in applications as handy tools to study the qualitative as well as quantitative properties of solutions of some stochastic di erential equations. We will use this inequalities to show the existence and uniqueness of solutions for nonlinear EDS. |
| Description: | In the theory of di erential equations the Gronwall’s lemma was widely used in various applications since its rst appearance in the article by Bellman [4] in 1943. In this article [4] the author gave a fundamental lemma of Gronwall–Bellman in order to study the stability and asymptotic behavior of solutions of di erential equations. In view of the important applications of the Gronwall–Bellman’s inequality, see [3]. The Gronwall lemma has seen several generalizations to various forms. In the stochastic eld, this lemma has its elds of application for the study of the existence and uniqueness of solutions of stochastic di erential equations (SDEs). Several forms of Gronwall inequality have been given for the integral of Itô [2, 6], in this paper we will give other forms of Gronwall inequality for the Itô and Startonovich integral nding their applications in various case to show the existence and uniqueness of solutions for nonlinear SDE. |
| URI: | http://dspace.univ-bouira.dz:8080/jspui/handle/123456789/10598 |
| Appears in Collections: | Articles |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| New inequalities of Gronwall type for the stochastic differential equations-1.pdf | In the theory of di erential equations the Gronwall’s lemma was widely used in various applications since its rst appearance in the article by Bellman [4] in 1943. In this article [4] the author gave a fundamental lemma of Gronwall–Bellman in order to study the stability and asymptotic behavior of solutions of di erential equations. In view of the important applications of the Gronwall–Bellman’s inequality, see [3]. The Gronwall lemma has seen several generalizations to various forms. In the stochastic eld, this lemma has its elds of application for the study of the existence and uniqueness of solutions of stochastic di erential equations (SDEs). Several forms of Gronwall inequality have been given for the integral of Itô [2, 6], in this paper we will give other forms of Gronwall inequality for the Itô and Startonovich integral nding their applications in various case to show the existence and uniqueness of solutions for nonlinear SDE. | 277,73 kB | Adobe PDF | View/Open |
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