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Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus
discrete Wick calculus fractional Brownian motion weak convergence
2010/10/19
We approximate the solution of some linear systems of SDEs driven by a fractional Brownian motion $B^H$ with Hurst parameter $H\in(\frac{1}{2},1)$ in the Wick--It\^{o} sense, including a geometric fra...
The Dimension of the Frontier of Planar Brownian Motion
Planar Brownian Motion Frontier Dimension Disconnection Exponents
2009/5/11
Let $B$ be a two dimensional Brownian motion and let the frontier of $B[0,1]$ be defined as the set of all points in $B[0,1]$ that are in the closure of the unbounded connected component of its comple...
Let $B(t)$ be a Brownian motion in $R^3$. A {it subpath} of the Brownian path $B[0,1]$ is a continuous curve $gamma(t)$, where $gamma[0,1] subseteq B[0,1]$ , $gamma(0) = B(0)$, and $gamma(1) = B(1)$. ...
Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon
Brownian motion finite horizon
2009/4/22
A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian mo- tion and its s...
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
stochastic fractional Brownian motion
2009/4/22
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...