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Keywords = p-mean μ-pseudo almost periodicity in distribution

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23 pages, 355 KB  
Article
Dynamic Behavior of Pseudo Almost Periodic Functions to Stochastic Differential Equations
by Zhonghua Wu
Symmetry 2025, 17(10), 1605; https://doi.org/10.3390/sym17101605 - 27 Sep 2025
Viewed by 360
Abstract
The main aim of this study is to create appropriate criteria for the existence of a unique μ-pseudo almost periodic solution to a particular type of stochastic differential equation, utilizing Bochner’s double sequences criterion, improved Gronwall’s lemma, Hölder’s inequality, and measure theory [...] Read more.
The main aim of this study is to create appropriate criteria for the existence of a unique μ-pseudo almost periodic solution to a particular type of stochastic differential equation, utilizing Bochner’s double sequences criterion, improved Gronwall’s lemma, Hölder’s inequality, and measure theory techniques. By applying the inequalities analysis condition and the fixed point theorem for contraction mapping, we can establish the existence of a single μ-pseudo almost periodic solution in distribution to the given stochastic equation. Finally, we use an example to demonstrate our stochastic processes. Full article
(This article belongs to the Section Mathematics)
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