I know that functions like `NDSolve`

can deal with delay differential equations and in the meanwhile, functions like `ItoProcess`

and `RandomFunction`

handle stochastic differential equations. So I wonder whether any built-in functions can handle it when the above two cases are combined together. For example, I naively tried the below codes by just slightly modifying the first example of `ItoProcess`

(`x[t] -> x[t - 1]`

in the square root)

`proc = ItoProcess[\[DifferentialD]x[t] == -x[t] \[DifferentialD]t + Sqrt[1 + x[t - 1]^2] \[DifferentialD]w[t], x[t], {x, 1}, t, w \[Distributed] WienerProcess[]] RandomFunction[proc, {0., 5., 0.01}] `

The first row of codes runs seemly well, but the second one just returns a `RandomFunction::unsproc`

error, specifically `RandomFunction::unsproc: The specification `<Ito process>` is not a random process recognized by the system.`

.

Or do I have to implement a version myself with Euler method alike?