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Two switching multiple disorder problems for Brownian motions
Multiple disorder problem optimal switching problem Brownian motion
2010/11/8
The multiple disorder problem seeks to determine a sequence of stopping times which are as close as possible to the unknown times of disorders at which the observation process changes its probability ...
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...
First of all we want to thank the editor, Michael Newton, for leading the review and discussion of our work.
Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation...
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...