Besicovitch Almost Periodic Solutions to Stochastic Dynamic Equations with Delays

• Yongkun Li ^[1] ; Xiaoli Huang ^[1]
  1. [1] Yunnan University

     Yunnan University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • In order to unify the study of Besicovitch almost periodic solutions of continuous time and discrete-time stochastic differential equations, we first propose concepts of Besicovitch almost periodic stochastic processes in p-th mean and of Besicovitch almost periodic stochastic processes in distribution on time scales, and reveal the relationship between the two random processes. Then, taking a class of stochastic Clifford-valued neural networks with time-varying delays on time scales as an example of stochastic dynamic equations with delays, we establish the existence and stability of Besicovitch almost periodic solutions in distribution for this class of networks by using Banach’s fixed point theorem, time scale calculus theory and inequality techniques.

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