Approximate Exit Probabilities for a Brownian Bridge on a Short Time Interval, and Applications.

Abstract

Let T be the first exit time of Brownian motion W(t) from a region R in d-dimensional Euclidean space having a smooth boundary. Given points xi sub o and xi sub 1 in R, ordinary and large deviation approximations are given for Pr(T<xi/W(0) = xi sub o, W(epsilon) = xi sub 1 as epsilon approaches limit of 0. Applications are given to hearing the shape of a drum, approximating the second virial coefficient, and Monte Carlo estimation of first passage distributions for Brownian motion.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1987
Accession Number
ADA179012

Entities

People

  • David Siegmund
  • H. R. Lerche

Organizations

  • Stanford University

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Brownian Motion
  • Computations
  • Coordinate Systems
  • Data Science
  • Estimators
  • Information Science
  • Military Research
  • Monte Carlo Method
  • Normal Distribution
  • Pregnancy Complications
  • Probability
  • Random Variables
  • Random Walk
  • Statistics
  • Time Intervals
  • United States

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Calculus or Mathematical Analysis
  • Statistical inference.

Technology Areas

  • Space