Random integrodifferential equations of Volterra type with delay : attractiveness and stability

作者：

Highlights：

• The existence and the uniqueness of mild solutions of random integrodifferential equations are studied

• We develop a new tool in the resolvent operator theory and apply several fixed-point theorems

• We establish the properties of mean-square stability and attractiveness

• We apply the theoretical outcomes to a type of the Heath-Jarrow-Morton-Musiela (HJMM) equation

摘要

•The existence and the uniqueness of mild solutions of random integrodifferential equations are studied•We develop a new tool in the resolvent operator theory and apply several fixed-point theorems•We establish the properties of mean-square stability and attractiveness•We apply the theoretical outcomes to a type of the Heath-Jarrow-Morton-Musiela (HJMM) equation

论文关键词：Volterra integral equation,Functional differential equation (FDE),Stochastic functional differential equation (SFDE),Delay,Mild Solution,Random fixed-point,Evolution family,Stability,Attractiveness

论文评审过程：Received 18 October 2021, Revised 4 May 2022, Accepted 4 June 2022, Available online 11 June 2022, Version of Record 11 June 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127301