{"title":"Characterization of Discrete-time Fractional Brownian motion","authors":"A. Gupta, S. Joshi","doi":"10.1109/INDCON.2006.302748","DOIUrl":null,"url":null,"abstract":"In this paper, we present the characterization of the discrete-time fractional Brownian motion (dfBm). Since, these processes are non-stationary; the auto-covariance matrix is a function of time. It is observed that the eigenvalues of the auto-covariance matrix of a dfBm are dependent on the Hurst exponent characterizing this process. Only one eigenvalue of this auto-covariance matrix depends on time index n and it increases as the time index of the auto-covariance matrix increases. All other eigenvalues are observed to be invariant with time index n in an asymptotic sense. The eigenvectors associated with these eigenvalues also have a fixed structure and represent different frequency channels. The eigenvector associated with the time-varying eigenvalue is a low pass filter","PeriodicalId":122715,"journal":{"name":"2006 Annual IEEE India Conference","volume":"23 3","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 Annual IEEE India Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/INDCON.2006.302748","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
In this paper, we present the characterization of the discrete-time fractional Brownian motion (dfBm). Since, these processes are non-stationary; the auto-covariance matrix is a function of time. It is observed that the eigenvalues of the auto-covariance matrix of a dfBm are dependent on the Hurst exponent characterizing this process. Only one eigenvalue of this auto-covariance matrix depends on time index n and it increases as the time index of the auto-covariance matrix increases. All other eigenvalues are observed to be invariant with time index n in an asymptotic sense. The eigenvectors associated with these eigenvalues also have a fixed structure and represent different frequency channels. The eigenvector associated with the time-varying eigenvalue is a low pass filter