Some views on recent randomized study of infinite dimensional functional differential equations

Abstract

As a relatively new area in mathematics, the subject of abstract or infinite dimensional stochastic functional differential equations is still in its tender age at present. In this note, the author intends to show some of his personal views, mainly based on his own academic experience in this topic, about the current art of research. Special attention is paid to a statement of various methods, techniques and ideas in the undergoing development. What I am trying to do is to highlight the coherent characterization of various difficult problems, effective methods and useful toods frequently seen in this subject. A mild notice is also made on some possible pitfalls which an active researcher working in this area should take into account. It is hoped that, through this short work, some more valuable developments can be promoted and significant progress can be expected in the future.