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

✍ Scribed by M. Cardenas; J.H. Matis

• Publisher: Springer
• Year: 1974
• Tongue: English
• Weight: 584 KB
• Volume: 36
• Category: Article
• ISSN: 1522-9602
• DOI: 10.1016/s0092-8240(74)80045-5

✦ Synopsis

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 an n-compartment catenary and to an n-compartment mammillary system. The multivariate distributions of these two systems are obtained under two sets of initial conditions: (1) the initial dintribution is known; and (2) the number of particles in each compartment of the system at time t = 0 is determined. The moments of these distributions are also produced and compared with existing results.