Generalize WienerProcess

Together the WhiteNoiseProcess, which includes the option of specifying a specific distribution for the noise, and the TransformProcess, which allows functions of processes, provide a great deal of flexibility in creating discrete-time processes.

There does not appear to be a similar approach to creating a custom continuous-time process. For instance, it would be nice it the WienerProcess function included an option to specify a distribution other than the Gaussian.

I see from other questions that the discrete-time processes can be converted into continuous time processes by using Interpolation; however, it’s not clear to me how to do this conversion in a way that the resulting process can be use with RandomFunction. To be more specific, while a Interpolation can be used to specify a specific conversion given {t_min, t_max, dt} it’s not clear how to define a general continuous time process that RandomFunction will recognize.