2014/02/10 by Kai Liu, Liu, Kai
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1402.2199
openalex publication_date 2014/02/10 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
This paper continues the study of [11, 13] for stationary solutions of\nstochastic linear retarded functional differential equations with the emphasis\non delays which appear in those terms including spatial partial derivatives. As\na consequence, the associated stochastic equations have unbounded operators\nacting on the discrete or distributed delayed terms, while the operator acting\non the instantaneous term generates a strongly continuous semigroup. We present\nconditions on the delay systems to obtain a unique stationary solution by\ncombining spectrum analysis of unbounded operators and stochastic calculus. A\nfew instructive cases are analyzed in detail to clarify the underlying\ncomplexity in the study of systems with unbounded delayed operators.\n