Thankfully the awful linear congruential generators of past have mostly been killed by now. Mersenne twister isn't ideal (kind of slow and uses a bunch of memory), but it is pretty solid. The xoshiro family also is pretty widely used in now for programming languages, and that's a major an improvement over lcg on all fronts (except roughly tied for speed).
Have they gotten one that implements well in a gpu yet? Last I read many people doing stochastic filters (resampling etc.) Were generating noise cpu side and shipping it over to the device. But that has been a while.
