The problem setting is quite general and as follows:
An infinite number of particles (probability density) is moving in 1d space, with force defined at each point by function F. It also undergoes diffusion by Brownian noise W. All boundary conditions are defined properly.
Are there approaches to find the distribution beyond Fokker Planck/forward Kolmogorov equations?
These may be however advanced, because the motivation is not the solution (that can be extracted directly with FP) but aggregation of tools.