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A process very similar to multifractional Brownian motion
Fractional Brownian motion wavelet series expansions multifractionalBrownian motion Holder regularity
2010/3/17
Multifractional Brownian motion (mBm), denoted here by X, is one
of the paradigmatic examples of a continuous Gaussian process whose pointwise
H¨older exponent depends on the location. Recall that X...
Some Extensions of Fractional Brownian Motion and Sub-Fractional Brownian Motion Related to Particle Systems
Brownian Motion three self-similar long-range dependence Gaussian processes
2009/3/23
In this paper we study three self-similar, long-range dependence, Gaussian processes. The first one, with covariance ∫0min(s,t) ua [(t-u)b+(s-u)b]du,parameters a > -1, -1 < b ≤ 1, |b| ≤ 1 + a, corresp...
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
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...