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?
