MIT Libraries homeMIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Power law Polya’s urn and fractional Brownian motion

Author(s)
Hammond, Alan; Sheffield, Scott Roger
Thumbnail
DownloadSheffield_Power law.pdf (311.7Kb)
OPEN_ACCESS_POLICY

Open Access Policy

Creative Commons Attribution-Noncommercial-Share Alike

Terms of use
Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
Metadata
Show full item record
Abstract
We introduce a natural family of random walks S[subscript n] on Z that scale to fractional Brownian motion. The increments X[subscript n] := S[subscript n] − S[subscript n]−1 ∈ {±1} have the property that given {X[subscript k] : k < n}, the conditional law of X[subscript n] is that of X[subscript n−k[subscript n]] , where k[subscript n] is sampled independently from a fixed law μ on the positive integers. When μ has a roughly power law decay (precisely, when μ lies in the domain of attraction of an α-stable subordinator, for 0 < α < 1/2) the walks scale to fractional Brownian motion with Hurst parameter α + 1/2. The walks are easy to simulate and their increments satisfy an FKG inequality. In a sense we describe, they are the natural “fractional” analogues of simple random walk on Z.
Date issued
2012-12
URI
http://hdl.handle.net/1721.1/93178
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Probability Theory and Related Fields
Publisher
Springer-Verlag
Citation
Hammond, Alan, and Scott Sheffield. “Power Law Polya’s Urn and Fractional Brownian Motion.” Probability Theory and Related Fields 157, no. 3–4 (December 11, 2012): 691–719.
Version: Original manuscript
ISSN
0178-8051
1432-2064

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries homeMIT Libraries logo

Find us on

Twitter Facebook Instagram YouTube RSS

MIT Libraries navigation

SearchHours & locationsBorrow & requestResearch supportAbout us
PrivacyPermissionsAccessibility
MIT
Massachusetts Institute of Technology
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.