In this paper, a Banach space framework is introduced in order to deal with finite-dimensional path-dependent stochastic differential equations. A version of Kolmogorov backward equation is formulated ...

Infinite-dimensional systems, characterised by state spaces of infinite dimension such as those described by partial differential equations, present profound challenges and opportunities within ...

Sufficient conditions are given for the existence, uniqueness and finite-dimensional approximation of the solution to a first-order infinite-dimensional vector differential equation. Given a suitable ...