Measure of noncompactness and application to stochastic differential equations

Advances in Difference Equations

Nadjeh Redjel¹  Abdelkader Dehici² 

[1]Department of Mathematics, University of Constantine 1, Constantine, Algeria

[2]Laboratory of Informatics and Mathematics, University of Souk-Ahras, Souk-Ahras, Algeria

关键词: Wiener process;    Itô integral;    Banach space;    fixed point;    existence;    uniqueness;    measure of noncompactness;    condensing operators;    Kirk’s process;    47H10;    47H08;    60H10;   

DOI  :  10.1186/s13662-016-0748-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY