Abstract
When the deoxygenation and reaeration coefficients and the initial conditions are random variables, a random differential equation arises whose mean square solution gives the biochemical oxygen demand (BOD) and dissolved oxygen deficit (OD) at downstream points from a source of pollution in a stream. A Liouville-type theorem is used to obtain the probability density function of the BOD and OD at each downstream point, completely characterizing the BOD and OD processes. Some examples, with computations of the means, variances, and marginal densities, are given and compared with previous results.
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