The One-Sided Barrier Problem for Gaussian Noise

1962/03/01 by David Slepian, D. Slepian · 9 citations
Decision Sciences · Economics, Econometrics and Finance · #Financial Risk and Volatility Modeling #Probabilistic and Robust Engineering Design #Stochastic processes and financial applications

paper · doi:10.1002/j.1538-7305.1962.tb02419.x

crossref issued 1962/03/01 · crossref published 1962/03/01 · crossref published-print 1962/03/01 · openalex publication_date 1962/03/01 · crossref published-online 2013/07/29 · crossref created 2013/07/29 · crossref deposited 2020/10/14 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/08/02

Abstract

This paper is concerned with the probability, P[T, r(τ)], that a stationary Gaussian process with mean zero and covariance function r(τ) be nonnegative throughout a given interval of duration T. Several strict upper and lower bounds for P are given, along with some comparison theorems that relate P's for different covariance functions. Similar results are given for F[T, r(τ)], the probability distribution for the interval between two successive zeros of the process.

Citations

• Mathematical Analysis of Random Noise

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