Having an engineering background, I would like to ask the more mathematically inclined experts.

One of the key parameters of a radio reception device is its bit error rate (BER) for a given ratio of wanted signal and disturbers like noise.
At the end of the chain of noisy amplifiers, filters, mixers and other nonlinearities, the ratio of correctly detected to sent bits is calculated.
These noisy nonlinear transient simulations have to be repeated multiple times to arrive at robust statistics.

Could StochasticDiffEq provide here a faster approach?
Are other methods known which could reduce the number of required simulations?

If your system can be described as a set of stochastic differential equations, then StochasticDiffEq can definitely be a way to accelerate the simulation process.

Yes, there are a few ways to to this. For one, the high weak order methods will have faster convergence in mean for higher dt, so you can increase dt above the simpler methods and still hit the required tolerance more quickly. Additionally, multilevel Monte Carlo methods can decrease the sampling error faster. This set of methods is not in the library yet, though I think @frankschae may have looked at it.

Thx Chris, will contact @frankschae.
On the higher order integrators, I wonder how they score in systems with a high switching rate. Modern receivers use a lot of switching mixers and switched/N-path filters, including jitter/phase noise.

Related: power systems simulators have a solution for the switching activity: they work on a fixed-step time grid and interpolate to the switching time instances (switched linear circuits).
Really curious to compare with JuliaSpice (for when?): to see if an llvm-assisted ODE solver can beat MNA+Markowitz !