“…This approach uses stochastic calculus to include environmental fluctuations or noise in a deterministic differential model [6,15,18,39,48]. The simple structure of basic model that describes the evolution of BOD has allowed this approach to be applied successfully and several works have appeared over the last two decades [17,22,23,27,28,40,46,54,55,57]. In particular, both Padget et al [28] and Finney et al [17], in their seminal works, formulated the Fokker-Plank equation for the Streeter-Phelps model [41] and were able to numerically compute the joint and marginal probability density functions of BOD and DO (i.e., dissolved oxygen) along a river with randomness in the initial conditions, inputs, and coefficients modelled as Gaussian white noise.…”