Asymptotically almost automorphic solutions to stochastic differential equations driven by a Lévy process |
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Authors: | Yong-Kui Chang Chao Tang |
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Institution: | 1. School of Mathematics and Statistics, Xidian University, Xi’an, P.R. China.;2. College of Mathematics, Sichuan University, Chengdu, P.R. China. |
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Abstract: | In this paper, a new concept of Poisson asymptotically almost automorphy for stochastic processes is introduced. And then, some fundamental properties including composition theorems for the space of such processes are proved. Subsequently, this concept is applied to investigate the existence and uniqueness of asymptotically almost automorphic solutions in distribution to some linear and semilinear stochastic differential equations driven by a Lévy process under some suitable conditions. Finally, an example is given to illustrate the main results. |
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Keywords: | Poisson asymptotically almost automorphy for stochastic processes stochastic differential equations Lévy process |
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