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On the stochastic theory of compartments: Solution forn-compartment systems with irreversible, time-dependent transition probabilities

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Abstract

The bivariate distribution of a two-compartment stochastic system with irreversible, time-dependent transition probabilities is obtained for any point in time. The mean and variance of the number of particles in any compartment and the covariance between the number of particles in each of the two compartments are exhibited and compared to existing results. The two-compartment system is then generalized to ann-compartment catenary and to ann-compartment mammillary system. The multivariate distributions of these two systems are obtained under two sets of initial conditions: (1) the initial distribution is known; and (2) the number of particles in each compartment of the system at timet=0 is determined. The moments of these distributions are also produced and compared with existing results.

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Authors and Affiliations

  1. Institute of Statistics, Texas A & M University, 77840, College Station, Texas

    M. Cardenas & J. H. Matis

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  1. M. Cardenas
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  2. J. H. Matis
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Cardenas, M., Matis, J.H. On the stochastic theory of compartments: Solution forn-compartment systems with irreversible, time-dependent transition probabilities. Bltn Mathcal Biology 36, 489–504 (1974). https://doi.org/10.1007/BF02463262

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  • DOI: https://doi.org/10.1007/BF02463262

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