Pseudo S-asymptotically Bloch type periodicity with applications to partial stochastic neutral evolution equations

Purpose This paper introduces the concept of (µ, ν)-pseudo S-asymptotically Bloch type (ω, k)- periodic functions, aiming to extend the framework of periodicity in stochastic analysis and to investigate their role in neutral partial stochastic differential equations in separable Hilbert spaces. Design/methodology/approach Using stochastic analysis techniques together with Banach’s fixed point Theorem, we establish rigorous conditions that guarantee the existence and uniqueness of p-mean (µ, ν)-pseudo S-asymptotically Bloch type (ω, k)-periodic mild solutions. Findings Our results show that, under suitable assumptions, these solutions not only exist uniquely but also exhibit global exponential stability. To illustrate the practical applicability of the theoretical findings, a detailed example is provided. Originality/value This work provides a new perspective on analyzing periodicity and stability in stochastic differential equations.