A Random Differential Equation Arising in Stream Pollution

[+] Author and Article Information
W. J. Padgett, S. D. Durham

Dept. of Mathematics and Computer Science, University of South Carolina, Columbia, S.C.

J. Dyn. Sys., Meas., Control 98(1), 32-36 (Mar 01, 1976) (5 pages) doi:10.1115/1.3426981 History: Received August 14, 1975; Online July 13, 2010


A new stochastic model for stream pollution is discussed. The model involves a random differential equation of the form X ̇(t) = AX (t) + y (t), 0 ≤ t ≤ Q, (for some large Q > 0) where X (t) is a two-dimensional vector-valued stochastic process with the first component giving the biochemical oxygen demand (BOD) and the second component representing the dissolved oxygen (DO) concentration at distance t downstream from a major source of pollution. Some recent theory of random equations is utilized to solve the random differential equation, and simulated trajectories of the BOD and DO processes are presented which illustrate the theoretical results.

Copyright © 1976 by ASME
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