I need to simulate a process of the form

$$X_t=\int_0^t f(s,t)\mathop{dW_s}$$

where $f$ is deterministic and the integral is an Itô integral. I know I can simply take finite Itô sums of discrete increments of the Brownian motion driver, but I am wondering if there are more sophisticated approaches. Common methods such as the Euler-Maruyama method do not appear to be applicable because the integrand depends on the upper terminal $t$ and so $X_t$ is not an Itô process.

Are there known approaches for simulating this kind of process?

(Answers to related questions that would help to find relevant literature would also be useful: eg. Does this kind of process have a name? Is there a way of writing it as a SDE? If so, does that class of SDEs have a name?)

**EDIT**

The particular integral I'm interested in is the Molchan-Golosov representation of fractional Brownian motion. Up to a multiplicative constant, this is $$\int_0^t (t-s)^{H-1/2}F(1/2-H,H-1/2,H+1/2,\frac{s-t}{s})\mathop{dW_s}$$ where $H\in(0,1)$ and $F$ is the Gauss hypergeometric function.

In further reading I have found that processes of this form are known as *Volterra processes*, but I haven't found any discussion of simulation algorithms.