The existence and uniqueness of solution for a class of stochastic functional equations on S. P. space (Q5959685)

Let \({\mathcal B}\) be a Banach space of all left-continuous \(({\mathcal I}_t)\)-adapted stochastic processes. The authors consider a stochastic functional equation \(X= \widetilde\Phi(X)\) with \(\widetilde\Phi:{\mathcal B}\to{\mathcal B}\). They study the existence and uniqueness of solution of this equation. This result is applied to some stochastic differential equations.