A general stochastic model for predicting BOD and DO in streams

The stochastic model presented in this study is a random differential equation of the form X(t) = A(t)X(t) + Y(t), t ≥ 0. with initial conditions X₀ = X(0). X(t) is a vector with biochemical oxygen demand (BOD) and dissolved Oxygen (DO) at a distance t downstream from the pollution source for components. The velocity of the stream is included in A(t) and is random and distance dependent. The initial amount of pollution is discharged over an interval (0,t_o ). Simulated trajectories for BOD and DO are computed.