DIFFUSION APPROXIMATIONS IN APPLIED PROBABILITY.
CORNELL UNIV ITHACA N Y DEPT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH
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This is an expository paper which discusses numerous methods for obtaining diffusion approximations for models in applied probability. For many such models it is difficult to obtain explicit expressions for the distributions of random quantities of interest. In some problems, however, approximations can be obtained from limit theorems as a particular physical parameter approaches a limit. Examples of such physical parameters are the traffic intensity and the number of servers in queueing models, the number of balls in various urn models, and the probability of breakdown in a quality control model. In general, the objective is to obtain limit theorems in the sense of weak convergence of measures for a sequence of stochastic processes. Often the limit process is a well-known diffusion process. This diffusion process then yields approximations in the same manner as does the central limit theorem. Author
- Statistics and Probability
- Operations Research