A stochastic model for bod and do when the discharged pollutants and the flow of the stream are random quantities

The stochastic model presented in this paper is a random differential equation of the form X(t) = AX(t) + Y(t), t ≥0, with initial conditionsX0 = 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 A vector and is considered a random variable. Also the initial conditions are considered random. Therefore, this model contains random initial conditions and random coefficients. Simulated trajectories of the BOD and DO processes are computed and some of their statistical properties are discussed.

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Presently at Department of Mathematics, The University of North Carolina at Charlotte, Charlotte N.C. 28223 (U.S.A.).