Stochastic model for BOD and DO in streams when the velocity is random and distance‐dependent

The stochastic model studied in this paper 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 incorporated into the vector A(t) and is random and distance dependent. The inhomogeneous term Y(t) and the initial conditions are random vectors. Therefore, this model contains random initial conditions, random coefficients and random inhomogeneous terms. Simulated trajectories of the BOD and DO are computed.