Doubly-weighted pseudo almost automorphic solutions for nonlinear stochastic differential equations driven by Lévy noise

Abstract

This paper introduces the definitions of Poisson doubly-weighted pseudo almost automorphy and doubly-weighted pseudo almost automorphy (DWPAA) in distribution. Based on some suitable assumptions, we establish some basic theory for these definitions, and investigate the existence, uniqueness and exponential stability of the DWPAA solution in distribution for a class of nonlinear stochastic differential equations driven by Lévy noise. Finally, an example is further given to illustrate the effectiveness of our results.

Keywords:

• Doubly-weighted pseudo almost automorphy
• Lévy noise
• mild solution
• existence and uniqueness
• exponential stability

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11671149]; the Science and the Technology Planning Project of Guangdong Province [grant number 2013B010101009]; Natural Science Foundation of Guangdong Province [grant number 2014A030313256], China.