Pseudo almost automorphy of stochastic neutral partial functional differential equations with Lévy noise

ABSTRACT

The paper introduces and studies the concepts of (Poisson) $({\mu }_1,{\mu }_2)$-pseudo almost automorphy of class r for stochastic processes. Under suitable conditions on the coefficients, we establish the existence, and uniqueness of mild solutions, which are $({\mu }_1,{\mu }_2)$-pseudo almost automorphic of class r in distribution for stochastic neutral partial functional differential equations with Lévy noise.

KEYWORDS:

• Poisson square-mean pseudo almost automorphy
• measure theory
• analytic semigroup
• Lévy noise

AMS SUBJECT CLASSIFICATIONS:

• 60H10
• 43A60

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by the Key Projects of Natural Science Foundation of Zhejiang Province [grant number LY19A010013] and the National Natural Science Foundation of China [grant number 11501507].