𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A reinforcement-depletion urn problem—I. Basic theory

✍ Scribed by L.R. Shenton

Publisher
Springer
Year
1981
Tongue
English
Weight
444 KB
Volume
43
Category
Article
ISSN
1522-9602

No coin nor oath required. For personal study only.

✦ Synopsis

An urn contains balls of different colors. Specified numbers of each color are added and form a reinforcement. The total reinforcement is randomly removed, forming a depletion. The process, not necessarily with the same reinforcements, is performed a number of times. The factorial moment generating function of the urn configurations at any stage is given in terms of multivariate difference operators. Cases when the reinforcement vector is defined as a stochastic variable are considered. The problem is a generalization of an urn model associated with radioactive atoms and stable atoms proposed by S. R. Bernard. The solutions given here have a definite application to the problem of modelling tracers in compartmental systems.

📜 SIMILAR VOLUMES

A reinforcement depletion urn problem-II
A reinforcement depletion urn problem-II. Application and generalization
✍ L.R. Shenton 📂 Article 📅 1983 🏛 Springer 🌐 English ⚖ 349 KB

The urn model discussed in part I is generalized so that the random depletion of balls from the urn in any cycle is not necessarily the same as the reinforcement in that cycle. This model is applied to an urn containing balls of three colors (white, red, black) for which the black balls always recei

A fluctuation problem in particle transp
A fluctuation problem in particle transport theory I
✍ M.M.R. Williams 📂 Article 📅 1977 🏛 Elsevier Science 🌐 English ⚖ 605 KB

The fluctuation in the number of collisions suffered by particles as they slow down in a moderating medium is studied via a probability balance equation. The equation describes the collision history of foreign particles slowing down in a host medium and also accounts for the recoil particles produce