Diffusion Bounds for some Passage Probabilities in the Theory of Storage.
Abstract
A storage process X(t) is considered with general jump size distribution, non-decreasing state-dependent output rate, and non-increasing state-dependent jump intensity. The object of study is U(x), the probability that state zero is never reached when starting from state x > 0. The natural diffusion approximation for X(t) is identified. An explicit formula is known for U sub * of x, the probability that the approximating diffusion process never reaches state zero when starting from state x > 0. It is shown that U sub * < or = U and a conjecture is advanced regarding conditions under which this bound is tight.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1976
- Accession Number
- ADA025728
Entities
People
- J. Michael Harrison
Organizations
- Stanford University