Abstract
A stochastic model for biochemical oxygen demand (BOD) and dissolved oxygen (DO) at a distance t downstream, when pollutants are discharged over a continuous stretch, is a random differential equation of the form X(t)=AX(t) + Y(t), t⩾0, with the initial condition X0 = X(0). Assuming that X0 is a random vector having a bivariate normal distribution with the mean vector μ0 and the precision (the inverse of the variance-covariance) matrix Λ0, we provide the prediction equation X(t) at any point t a for μ0 keeping Λ0 fixed and known, and (ii) a normal-Wishart prior for (μ0, Λ0. The theory is supplemented by numerical studies.
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