Square-mean weighted pseudo almost automorphic solutions for stochastic semilinear integral equations

2014/06/16 by Kexue Li, Jigen Peng, Li, Kexue +1
Computer Science · Engineering · Mathematics · #34F05 #FOS: Mathematics #Neural Networks Stability and Synchronization #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations #math.PR #msc:34F05

paper · pdf · doi:10.48550/arxiv.1406.4003

arxiv created 2014/06/16 · openalex publication_date 2014/06/16 · arxiv updated 2014/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the concept of S²-weighted pseudo almost automorphy for stochastic processes. We study the existence and uniqueness of square-mean weighted pseudo almost automorphic solutions for the semilinear stochastic integral equation x(t)=∫_-∞^ta(t-s)[Ax(s)+f(s,x(s))]ds+∫_-∞^ta(t-s)φ(s,x(s))dw(s), t∈ℝ, where a∈ L¹(ℝ₊), A is the generator of an integral resolvent family on a Hilbert space H, w(t) is the two-sided Q-Wiener process, f,φ: ℝ× L²(P,H)→ L²(P,H) are two S²-weighted pseudo almost automorphic functions.

Related

• Square-mean weighted pseudo almost automorphic solutions for nonautonomous stochastic differential equations driven by Levy noise
• Almost automorphy and various extensions for stochastic processes
• Square-mean almost automorphic solutions for some stochastic differential equations
• On weighted pseudo almost automorphic mild solutions for some mean field stochastic evolution equations
• Existence of almost automorphic solution in distribution for a class of stochastic integro-differential equation driven by Levy noise