Representations of fractional Brownian motion using vibrating strings

K. Dzhaparidze, J.H. van Zanten, P. Zareba

Research output: Contribution to JournalArticleAcademicpeer-review

201 Downloads (Pure)

Abstract

In this paper, we show that the moving average and series representations of fractional Brownian motion can be obtained using the spectral theory of vibrating strings. The representations are shown to be consequences of general theorems valid for a large class of second-order processes with stationary increments. Specifically, we use the 1-1 relation discovered by M.G. Krein between spectral measures of continuous second-order processes with stationary increments and differential equations describing the vibrations of a string with a certain length and mass distribution. © 2005 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)1928-1953
JournalStochastic Processes and Their Applications
Volume115
Issue number12
DOIs
Publication statusPublished - 2005

Bibliographical note

MR2178502

Fingerprint Dive into the research topics of 'Representations of fractional Brownian motion using vibrating strings'. Together they form a unique fingerprint.

Cite this