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

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Diffusion
  • Probability

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.