Stepanov‐like doubly weighted pseudo almost automorphic processes and its application to Sobolev‐type stochastic differential equations driven by G‐Brownian motion |
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Authors: | Qigui Yang Ping Zhu |
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Affiliation: | Department of Mathematics, South China University of Technology, Guangzhou, China |
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Abstract: | This paper investigates the properties of the p‐mean Stepanov‐like doubly weighted pseudo almost automorphic (SpDWPAA) processes and its application to Sobolev‐type stochastic differential equations driven by G‐Brownian motion. We firstly prove the equivalent relation between the SpDWPAA and Stepanov‐like asymptotically almost automorphic stochastic processes based on ergodic zero set. We further establish the completeness of the space and the composition theorem for SpDWPAA processes. These results obtained improve and extend previous related conclusions. As an application, we show the existence and uniqueness of the Sp DWPAA solution for a class of nonlinear Sobolev‐type stochastic differential equations driven by G‐Brownian motion and present a decomposition of this unique solution. Moreover, an example is given to illustrate the effectiveness of our results. |
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Keywords: | completeness composition theorems existence and uniqueness G‐Brownian motion Stepanov‐like doubly weighted pseudo almost automorphy |
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