Stochastic models for first-order kinetics of biochemical oxygen demand with random initial conditions, inputs, and coefficients (Q1112767)

Biochemical oxygen demand (BOD) is a parameter of prime importance in surface water pollution studies and in the design and operation of waste- water treatment plants. A general, stochastic analytical model (denoted S1) is developed for the temporal expectation and (heteroscedastic) variance of first-order BOD kinetics. The model is obtained by integrating the moment equation, which is derived from the mathematical theory of stochastic differential equations. This model takes into account random initial conditions, random inputs, and random coefficients, which appear in the model formulation as initial condition \((\sigma^ 2_ 0)\), input \((\sigma^ 2_{\ell})\), and coefficient \((\sigma^ 2_ c)\) variance parameters, respectively.