A Non-Linear Renewal Theory with Applications to Sequential Analysis II.

Abstract

An analogue of Blackwell's renewal theorem is obtained for processes Z sub n = S sub n + xi sub n, where S sub n is the nth partial sum of a sequence X1,X2,... of independent identically distributed random variables with finite positive mean and xi sub n is independent of X sub n+1, X sub n+2,.. and has sample paths which are slowly changing in a sense made precise below. As a consequence, asymptotic expansions up to terms tending to 0 are obtained for the expected value of certain first passage times. Applications to sequential analysis are given.

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Document Details

Document Type
Technical Report
Publication Date
May 03, 1977
Accession Number
ADA049783

Entities

People

  • David Siegmund
  • T. L. Lai

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Analogs
  • Asymptotic Series
  • Boundaries
  • Data Science
  • Inequalities
  • Information Science
  • New York
  • Numbers
  • Probability
  • Probability Distributions
  • Random Variables
  • Random Walk
  • Sequences
  • Sequential Analysis
  • Statistics
  • Stochastic Processes
  • United States

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Mathematics or Statistics