Storage Theory and the Suprema of Certain Infinitely Divisible Processes

Abstract

Let X = (X(t), t > or = O) be a process with stationary, independent increments and no negative jumps. Let W = (W(t), t > or = O) be this same process modified by a reflecting barrier at zero (a storage process). Assuming that -E(X(t)) = mu > O, let M = sup(X(t):t > or = O), and denote by Phi(Alpha) the exponent function of X. A simple formula is derived for the Laplace transform of E(W(t)), t > or =, as a function of W(O).

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1976
Accession Number
ADA030648

Entities

People

  • J. M. Harrison

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • California
  • Distribution Functions
  • Governments
  • Markov Chains
  • Markov Processes
  • Military Research
  • Operations Research
  • Probability
  • Probability Distributions
  • Stationary
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Mathematical Modeling and Probability Theory.