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Erratum: A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand


 
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1. Title Title of document Erratum: A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
 
2. Creator Author's name, affiliation, country Carl Mueller; University of Rochester; United States
 
2. Creator Author's name, affiliation, country Zhixin Wu; DePauw University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) heat equation ; white noise ; stochastic partial differential equations
 
3. Subject Subject classification 60H15; 35R60; 35K05
 
4. Description Abstract

We give a new representation of fractional Brownian motion with Hurst parameter H<1/2 using stochastic partial differential equations.  This representation allows us to use the Markov property and time reversal, tools which are not usually available for fractional Brownian motion.  We then give simple proofs that fractional Brownian motion does not hit points in the critical dimension, and that it does not have double points in the critical dimension.  These facts were already known, but our proofs are quite simple and use some ideas of Lévy.

This is an Erratum for ECP volume 14 paper number 6.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF, NSA
 
7. Date (YYYY-MM-DD) 2012-01-30
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1774
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-1774
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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