2019/02/12 by Hailong Zhu, Zhu, Hailong
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1902.04199
openalex publication_date 2019/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For linear stochastic differential equations (SDEs) with bounded coefficients, we establish the robustness of nonuniform mean-square exponential dichotomy (NMS-ED) on [t0,+\oo), (-\oo,t0] and the whole \R separately, in the sense that such an NMS-ED persists under a sufficiently small linear perturbation. The result for the nonuniform mean-square exponential contraction (NMS-EC) is also discussed. Moreover, in the process of proving the existence of NMS-ED, we use the observation that the projections of the "exponential growing solutions" and the "exponential decaying solutions" on [t0,+\oo), (-\oo,t0] and \R are different but related. Thus, the relations of three types of projections on [t0,+\oo), (-\oo,t0] and \R are discussed.