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The Chance of a Long Lifetime for Brownian Motion in a Horn-Shaped Domain
Brownian Motion horn-shaped domain conditioning comparison argument
2009/3/23
By means of a simple conditioning/comparison argument, we derive the chance of a long lifetime for Brownian motion in a horn-shaped domain
Survival probabilities for branching Brownian motion with absorption
Survival probability branching Brownian motion absorption
2009/3/23
We study a branching Brownian motion (BBM) with absorption, in which particles move as Brownian motions with drift $-rho$, undergo dyadic branching at rate $beta>0$, and are killed on hitting the orig...
Distribution of the Brownian motion on its way to hitting zero
Brownian motion probability density
2009/3/23
For the one-dimensional Brownian motion $B=(Bt)t≥ 0$, started at $x>0$, and the first hitting time $τ=inf{t≥ 0:Bt=0}$, we find the probability density of $Buτ$ for a $uin(0,1)$, i.e. of the Brownian ...
Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
Hermite power variation fractional Brownian motion
2009/3/20
Let q≥2 be a positive integer, B be a fractional Brownian motion with Hurst index H∈(0,1), Z be an Hermite random variable of index q, and Hq denote the q-th Hermite polynomial. For any n≥1, set Vn=∑0...
Exact confidence intervals for the Hurst parameter of a fractional Brownian motion
Concentration Inequalities Exact confidence intervals Fractional Brownian motion Hurst parameter
2010/3/17
In this short note, we show how to use concentration inequalities in order to build exact
confidence intervals for the Hurst parameter associated with a one-dimensional fractional Brownian motion.
Analytic crossing probabilities for certain barriers by Brownian motion
Brownian motion boundary-crossing probability moving barrier first hitting time density last exit time density Schwartz distribution
2010/4/28
We calculate crossing probabilities and one-sided last exit time
densities for a class of moving barriers on an interval [0,T] via Schwartz
distributions. We derive crossing probabilities and first ...
Identification of the multiscale fractional Brownian motion with biomechanical applications
Biomechanics Detection of change Goodness-of-fit test Fractional Brownian motion Semi-parametric estimation Wavelet analysis
2010/4/26
In certain applications, for instance biomechanics, turbulence, finance, or Internet traffic, it seems suitable to model the data by a generalization of a fractional Brownian motion for which the Hurs...