Diffusion Bounds for some Passage Probabilities in the Theory of Storage.
STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
Pagination or Media Count:
A storage process Xt 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 Ux, the probability that state zero is never reached when starting from state x 0. The natural diffusion approximation for Xt 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.
- Statistics and Probability