Deterministic and Stochastic Functional Differential Equations With Delay

The aim of this book is to provide an accessible treatment of stochastic functional differential equations with delay on infinite-dimensional spaces, such as Banach spaces. It systematically explores the approaches of fundamental solutions and evolutionary semigroups for semi-linear delay differential equations in abstract spaces, which are especially applicable to stochastic partial differential equations with time delay. A distinctive feature of this book is its special attention to systems with unbounded operators in the delay terms, encompassing as particular cases the usual systems considered in the popular monographs by J. Hale and J. H. Wu, as well as to the qualitative properties of these systems, such as their large-time asymptotic behaviour.