Two Barriers Problem for Continuously Differentiable Processes

Abstract

Durbin has presented a compact formula for the first passage density of a Gaussian process, which is locally like Brownian motion, to a smooth barrier. In previous works, we have extended the formula to the case of processes which are smooth functions of a continuously differentiable Gaussian vector process and to more general kinds of first passage time problems, so called marked crossings. In the present paper we obtain similar results for the first passage density in presence of a second absorbing barrier and use it to construct upper and lower bounds for the first passage, rainflow cycle amplitude, zerocrossing wave-length and amplitude densities. Numerical examples illustrate the results.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1989
Accession Number
ADA218564

Entities

People

  • Igor Rychlik

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Amplitude
  • Counting Methods
  • Covariance
  • Crossings
  • Data Science
  • Ergodic Processes
  • Fatigue Life
  • Gaussian Processes
  • Information Science
  • North Carolina
  • Probability
  • Random Variables
  • Statistical Analysis
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Statistical inference.