Solutions of stochastic differential-functional equations via bounded stochastic integral contractors (Q1194474)

Bounded stochastic integral contractors are used to establish the existence and uniqueness of the solution of a general stochastic differential-functional equation \(d\varphi(t)=F(D(\varphi_ t),dt)\), where \(\varphi_ t=\{\varphi(t-s): -\tau\leq s\leq 0\}\), \(D: C([- \tau,0],\mathbb{R}^ d)\to\mathbb{R}^ m\), and \(F(x,t)\) is a \(d\)-dimensional continuous \(C\)-semi-martingale with spatial parameter \(x\in\mathbb{R}^ m\). The integral here is a nonlinear stochastic integral. An application to stochastic differential equations is provided, and the theory is illustrated by an example.