Dynamic Behavior of Pseudo Almost Periodic Functions to Stochastic Differential Equations

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.