2011/06/08 by Kai Liu, Liu, Kai
Economics, Econometrics and Finance · Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods in inverse problems #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1106.1509
openalex publication_date 2011/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, some regularity properties of mild solutions for a class of\nstochastic linear functional differential equations driven by infinite\ndimensional Wiener processes are considered. In terms of retarded fundamental\nsolutions, we introduce a class of stochastic convolutions which naturally\narise in the solutions and investigate their Yosida approximants. By means of\nthe retarded fundamental solutions, we find conditions under which each mild\nsolution permits a continuous modification. With the aid of Yosida\napproximation, we study two kinds of regularity properties, temporal and\nspatial ones, for the retarded solution processes. By employing a factorization\nmethod, we establish a retarded version of Burkholder-Davis-Gundy's inequality\nfor stochastic convolutions.\n