The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes

Lorna R.M. Wilson, Keith I. Hopcraft, Eric Jakeman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The problem of zero-crossings is of great historical prevalence and promises extensive application. The challenge is to identify the Probability Density Function (PDF) for the times between successive zero-crossings of a stochastic process. In this paper, we address the zero-crossing problem for a Gaussian process and investigate the effect of introducing oscillations into the prescribed auto-correlation function. Statistics for the number of zero-crossings occurring within a set time period are calculated and verified by simulations of the process. We find that highly oscillatory auto-correlation functions cause realizations of the stochastic process to become increasingly 'regular' or 'deterministic'. Zeros occur at more regular intervals, implying that the inter-event PDF has an exponential tail with large persistence exponent. The persistence exponent exhibits a complex phenomenology that is strongly influenced by the oscillatory nature of the auto-correlation function. Comparison is made between the theoretical predictions and numerical simulation results.

LanguageEnglish
Title of host publicationVulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management
Subtitle of host publicationProceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA)
EditorsMichael Beer, Sui-Kui Au, Jim W. Hall
Place of PublicationReston, Virginia, USA
PublisherAmerican Society of Civil Engineers (ASCE)
Pages1856-1865
Number of pages10
ISBN (Print)9780784413609
DOIs
StatusPublished - 7 Jul 2014
Event2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014 - Liverpool, UK United Kingdom
Duration: 13 Jul 201416 Jul 2014

Conference

Conference2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014
CountryUK United Kingdom
CityLiverpool
Period13/07/1416/07/14

Fingerprint

Autocorrelation
Random processes
Probability density function
Statistics
Computer simulation

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality

Cite this

Wilson, L. R. M., Hopcraft, K. I., & Jakeman, E. (2014). The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes. In M. Beer, S-K. Au, & J. W. Hall (Eds.), Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA) (pp. 1856-1865). Reston, Virginia, USA: American Society of Civil Engineers (ASCE). https://doi.org/10.1061/9780784413609.186

The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes. / Wilson, Lorna R.M.; Hopcraft, Keith I.; Jakeman, Eric.

Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). ed. / Michael Beer; Sui-Kui Au; Jim W. Hall. Reston, Virginia, USA : American Society of Civil Engineers (ASCE), 2014. p. 1856-1865.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Wilson, LRM, Hopcraft, KI & Jakeman, E 2014, The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes. in M Beer, S-K Au & JW Hall (eds), Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). American Society of Civil Engineers (ASCE), Reston, Virginia, USA, pp. 1856-1865, 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014, Liverpool, UK United Kingdom, 13/07/14. https://doi.org/10.1061/9780784413609.186
Wilson LRM, Hopcraft KI, Jakeman E. The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes. In Beer M, Au S-K, Hall JW, editors, Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). Reston, Virginia, USA: American Society of Civil Engineers (ASCE). 2014. p. 1856-1865 https://doi.org/10.1061/9780784413609.186
Wilson, Lorna R.M. ; Hopcraft, Keith I. ; Jakeman, Eric. / The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes. Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). editor / Michael Beer ; Sui-Kui Au ; Jim W. Hall. Reston, Virginia, USA : American Society of Civil Engineers (ASCE), 2014. pp. 1856-1865
@inproceedings{8d4cb796b7b4478c84f29af16c8ecacb,
title = "The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes",
abstract = "The problem of zero-crossings is of great historical prevalence and promises extensive application. The challenge is to identify the Probability Density Function (PDF) for the times between successive zero-crossings of a stochastic process. In this paper, we address the zero-crossing problem for a Gaussian process and investigate the effect of introducing oscillations into the prescribed auto-correlation function. Statistics for the number of zero-crossings occurring within a set time period are calculated and verified by simulations of the process. We find that highly oscillatory auto-correlation functions cause realizations of the stochastic process to become increasingly 'regular' or 'deterministic'. Zeros occur at more regular intervals, implying that the inter-event PDF has an exponential tail with large persistence exponent. The persistence exponent exhibits a complex phenomenology that is strongly influenced by the oscillatory nature of the auto-correlation function. Comparison is made between the theoretical predictions and numerical simulation results.",
author = "Wilson, {Lorna R.M.} and Hopcraft, {Keith I.} and Eric Jakeman",
year = "2014",
month = "7",
day = "7",
doi = "10.1061/9780784413609.186",
language = "English",
isbn = "9780784413609",
pages = "1856--1865",
editor = "Michael Beer and Sui-Kui Au and Hall, {Jim W.}",
booktitle = "Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management",
publisher = "American Society of Civil Engineers (ASCE)",
address = "USA United States",

}

TY - GEN

T1 - The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes

AU - Wilson, Lorna R.M.

AU - Hopcraft, Keith I.

AU - Jakeman, Eric

PY - 2014/7/7

Y1 - 2014/7/7

N2 - The problem of zero-crossings is of great historical prevalence and promises extensive application. The challenge is to identify the Probability Density Function (PDF) for the times between successive zero-crossings of a stochastic process. In this paper, we address the zero-crossing problem for a Gaussian process and investigate the effect of introducing oscillations into the prescribed auto-correlation function. Statistics for the number of zero-crossings occurring within a set time period are calculated and verified by simulations of the process. We find that highly oscillatory auto-correlation functions cause realizations of the stochastic process to become increasingly 'regular' or 'deterministic'. Zeros occur at more regular intervals, implying that the inter-event PDF has an exponential tail with large persistence exponent. The persistence exponent exhibits a complex phenomenology that is strongly influenced by the oscillatory nature of the auto-correlation function. Comparison is made between the theoretical predictions and numerical simulation results.

AB - The problem of zero-crossings is of great historical prevalence and promises extensive application. The challenge is to identify the Probability Density Function (PDF) for the times between successive zero-crossings of a stochastic process. In this paper, we address the zero-crossing problem for a Gaussian process and investigate the effect of introducing oscillations into the prescribed auto-correlation function. Statistics for the number of zero-crossings occurring within a set time period are calculated and verified by simulations of the process. We find that highly oscillatory auto-correlation functions cause realizations of the stochastic process to become increasingly 'regular' or 'deterministic'. Zeros occur at more regular intervals, implying that the inter-event PDF has an exponential tail with large persistence exponent. The persistence exponent exhibits a complex phenomenology that is strongly influenced by the oscillatory nature of the auto-correlation function. Comparison is made between the theoretical predictions and numerical simulation results.

UR - http://www.scopus.com/inward/record.url?scp=84933557974&partnerID=8YFLogxK

U2 - 10.1061/9780784413609.186

DO - 10.1061/9780784413609.186

M3 - Conference contribution

SN - 9780784413609

SP - 1856

EP - 1865

BT - Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management

A2 - Beer, Michael

A2 - Au, Sui-Kui

A2 - Hall, Jim W.

PB - American Society of Civil Engineers (ASCE)

CY - Reston, Virginia, USA

ER -