Measure of noncompactness and application to stochastic differential equations

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• 作者：Abdelkader Dehici ; Nadjeh Redjel
• 关键词：47H10 ; 47H08 ; 60H10 ; Wiener process ; Itô integral ; Banach space ; fixed point ; existence ; uniqueness ; measure of noncompactness ; condensing operators ; Kirk’s process
• 刊名：Advances in Difference Equations
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,608 KB
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• 作者单位：Abdelkader Dehici (1) (2)
  Nadjeh Redjel (1) (2)
  
  1. Laboratory of Informatics and Mathematics, University of Souk-Ahras, P.O. Box 1553, Souk-Ahras, 41000, Algeria
  2. Department of Mathematics, University of Constantine 1, Constantine, 25000, Algeria
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In this paper, we study the existence and uniqueness of the solution of stochastic differential equation by means of the properties of the associated condensing nonexpansive random operator. Moreover, by taking account of the results of Diaz and Metcalf, we prove the convergence of Kirk’s process to this solution for small times. Keywords Wiener process Itô integral Banach space fixed point existence uniqueness measure of noncompactness condensing operators Kirk’s process