Generalized polynomial chaos for nonlinear random delay differential equations

In this paper, the generalized polynomial chaos (gPC) method is extended to solve nonlinear random delay differential equations (NRDDEs). The error estimation of the method is derived, which arises mainly from a finite-dimensional noise assumption, projection error and discretization error. When the error from the finite-dimensional noise assumption can not be omitted, the error of the method converges to a limit inferior which is just the error from the finite-dimensional noise assumption. With some numerical experiments, the obtained theoretical results are further illustrated.