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The estimation of parameters for a commonly used stochastic model



A region into which particles arrive in a random manner, remain a random amount of time, and then leave is considered. This model is used in penetration theories of heat and mass transfer. From observations of the number of particles present at any time, it is desired to estimate arrival and exit statistics, residence time statistics, and average rates of transfer across the region. Assuming arrival is a Poisson process, equations governing the above statistics are derived. Some problems in spectral analysis arising from the use of nondifferentiable stochastic processes are solved. Estimators for important parameters are discussed, and it is shown that generally they are biased. A derivation linking the rate of transfer across the region with the rates of transfer of particles is obtained and compared with other such results.

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