Document Type
Article
Publication Date
2012
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 Levy.
Recommended Citation
Z. Wu and C. Mueller (2nd Version) A connection between the Stochastic Heat Equation and Fractional Brownian Motion, and a simple proof of a result of Talagrand, appeared in “Electronic Communications on Probability” (peer-reviewed journal) and “ArXive” Volume 17 (2012) no.8 page 1-10, ISSN: 1083-589X
