A Note on First Passage Times in Birth and Death and Nonnegative Diffusion Processes.

Abstract

Consider a birth and death process starting in state 0. Analytical arguments were shown earlier that the time of first passage into state n has an increasing failure rate (IFR) distribution. We present a probabilistic proof for this. In addition, our proof shows that for a nonnegative diffusion process, the first passage time from state 0 to any state x is IFR.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1979
Accession Number
ADA080115

Entities

People

  • Cyrus Derman
  • Sheldon M. Ross
  • Zvi Schechner

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • California
  • Civil Engineering
  • Contracts
  • Diffusion
  • Engineering
  • Governments
  • Industrial Engineering
  • Markov Processes
  • Military Research
  • New York
  • Operations Research
  • Probability
  • Random Variables
  • Scientific Research
  • Systems Engineering
  • United States

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.