Sunset over Brownistan

Abstract

Consider a Brownian motion with a downward drift of rate a. Its maximum over all time has the exponential distribution with parameter 2a. Our aim is to study this maximum as a stochastic process indexed by a. That process is related to the convex majorant of the standard Brownian motion and, through the latter, to a Poisson random measure. This connection is exploited to obtain various distributional results. The results are of interest in queueing theory. Keywords: Brownian motion, Convex majorant, Poisson random measures, Stochastic geometry, Storage allocation.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1988
Accession Number
ADA198443

Entities

People

  • Erhan Cinlar

Organizations

  • Princeton University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Civil Engineering
  • Classification
  • Computational Complexity
  • Data Science
  • Markov Chains
  • Markov Processes
  • Observation
  • Operations Research
  • Probability
  • Random Variables
  • Security
  • Standards
  • Stationary
  • Stochastic Processes
  • Transitions
  • Universities

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.