Prefer a chat interface with context about you and your work?
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
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 …