STOCHASTIC MODELS FOR THE DISTRIBUTION OF RADIOACTIVE MATERIAL IN A CONNECTED SYSTEM OF COMPARTMENTS

摘要

A generalized Stochastic model is studied, relating to the decay of radioactive material in a compartmental system;this being a continuation of the work for a two compartment model initiated by Bernard and Uppulurl (1964, ORNL-3697 PP. 193-198).nThis led to the study of simultaneous Stochastic difference equations of random vectors, such as Cm = rm Cm-1,m = 1,2..., in which Cm represents a state of the system at the mth stage and rm is a matrix with random elements.nFrom this a recursive multivariate functional equation can be set up between the joint characteristic functions of the components in C and C. Expressions are derived for the means and covariances of the components of the vector C.nLastly, a continuous model involving the solution of a system of first order linear differential equations is studied and solutions derived in simple cases. In the appendix, the three compartment model is discussed in full detail and the feasibility of the model is studied.