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

   
@article{ECP1403,
	author = {Carl Mueller and Zhixin Wu},
	title = {A connection between the stochastic heat equation and fractional  Brownian motion, and a simple proof of a result of Talagrand},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {14},
	year = {2009},
	keywords = {heat equation, white noise, stochastic partial differential equations},
	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.
},
	pages = {no. 6, 55-65},
	issn = {1083-589X},
	doi = {10.1214/ECP.v14-1403},    
        url = {http://ecp.ejpecp.org/article/view/1403}}