Corrected Diffusion Approximations to First Passage Times.

Abstract

Section 1 in this document takes up the question of finding the distribution of excess over the boundary for random walks normalized to converge to a Wiener process. In some cases, such as tests of power 1 which are discussed in Section 2, the connection of the excess over the boundary to the problem of finding the correction to the Wiener process crossing time is simple and direct, and in other cases, especially that of Siegmund (1979), quantities with the excess over the boundary appear in ways that do not shed much light on the general problem. Section 3 gives a heuristic method for correcting the random walk probabilities, based on a reflection principle method of Siegmund and Yuh, which is the author's best idea for connection between the excess over the boundary and the corrected diffusion approximations to the hitting times in the general case.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1984
Accession Number
ADA140940

Entities

People

  • M. L. Hogan

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Crossings
  • Data Science
  • Diffusion
  • Distribution Functions
  • Equations
  • Identities
  • Information Science
  • Integral Equations
  • Normal Distribution
  • Probability
  • Random Variables
  • Random Walk
  • Sequential Analysis
  • Statistics
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Plasma Physics.
  • Statistical inference.
  • Systems Analysis and Design