I'm looking for a reference that would discuss a Stieltjes convolution with a white noise process. Additionally, I had a question about Stieltjes convolution.

Is Stieltjes convolution with a white noise process, $W(t)$ commutative?

if $F(t) \bigotimes W(t)=\int F(t-x)dW(x)$

then does $W(t) \bigotimes F(t)= \int W(t-x)dF(x) = F(t) \bigotimes W(t) $?

Additionally, I'd like to evaluate this integral numerically when I have no formula for F, but a list of points ${t_0,t_1,...t_{N-1} }$ and the values of $F(t)$ at those points. Any references that would point me in this direction would be appreciated.