Besicovitch almost periodic stochastic processes and almost periodic solutions of Clifford-valued stochastic neural networks

Abstract

<p style='text-indent:20px;'>In this paper, to begin with, we introduce the concept of Besicovitch almost periodic stochastic processes in distribution sense and study the relationship between it and the concept of Besicovitch almost periodic stochastic processes in <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-th mean sense. In addition, we take a class of Clifford-valued stochastic neural networks with time-varying delays as an example to investigate the existence and uniqueness of Besicovitch almost periodic solutions in distribution sense of this class of neural networks by using Banach fixed point theorem and a variant of Gronwall lemma. Moreover, we study the global exponential stability of this unique Besicovitch almost periodic solution in distribution sense by using inequality techniques. Finally, we give an example to illustrate our results. The results of this paper are completely new.</p>