Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 13C / d / Solution

With $A_i=a_{ij}{x}_j$ and constant $B_{ij}=b_{ij}$, the Fokker-Planck probability current becomesIn the stationary state we impose the stronger zero-current condition $J_i=0$, corresponding to detailed balance.