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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 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 E Mueller; University of Rochester
 
2. Creator Author's name, affiliation, country Zhixin Wu; DePauw University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) heat equation, white noise, stochastic partial differential equations
 
3. Subject Subject classification Primary, 60H15; Secondary, 35R60, 35K05.
 
4. Description Abstract

We give a new representation of fractional Brownian motion with Hurst parameter $H\leq\frac{1}{2}$ 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.

An Erratum is available in ECP volume 17 paper number 8.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSA, NSF
 
7. Date (YYYY-MM-DD) 2009-02-12
 
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/1403
 
10. Identifier Digital Object Identifier 10.1214/ECP.v14-1403
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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