Unilateral Small Deviations for the Integral of Fractional Brownian Motion

Details Unilateral Small Deviations for the Integral of Fractional Brownian Motion Unilateral Small Deviations for the Integral of Fractional Brownian Motion

2003-10-26

arxiv.org/abs/math/0310413v1

Mathematics

Probability

15 pages, 4 figures

Scientific paper

We consider the paths of a Gaussian random process $x(t)$, $x(0)=0$ not exceeding a fixed positive level over a large time interval $(0,T)$, $T\gg 1$. The probability $p(T)$ of such event is frequently a regularly varying function at $\infty$ with exponent $\theta$. In applications this parameter can provide information on fractal properties of processes that are subordinate to $x(\cdot)$. For this reason the estimation of $\theta$ is an important theoretical problem. Here, we consider the process $x(t)$ whose derivative is fractional Brownian motion with self-similarity parameter $0

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