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2009 A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
Carl Mueller, Zhixin Wu
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Electron. Commun. Probab. 14: 55-65 (2009). DOI: 10.1214/ECP.v14-1403

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 (http://dx.doi.org/10.1214/ECP.v17-1774)

Citation

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Carl Mueller. Zhixin Wu. "A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand." Electron. Commun. Probab. 14 55 - 65, 2009. https://doi.org/10.1214/ECP.v14-1403

Information

Accepted: 12 February 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1190.60053
MathSciNet: MR2481666
Digital Object Identifier: 10.1214/ECP.v14-1403

Subjects:
Primary: 60H15
Secondary: 35K05, 35R60

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