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            <title xml:lang="en">Pickands' constant at first order in an expansion around Brownian motion</title>
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                <forename type="first">Mathieu</forename>
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            <idno type="halRefHtml">&lt;i&gt;Journal of Physics A: Mathematical and Theoretical&lt;/i&gt;, 2017, 50 (16), pp.16LT04. &lt;a target="_blank" href="https://dx.doi.org/10.1088/1751-8121/aa5c98"&gt;&amp;#x27E8;10.1088/1751-8121/aa5c98&amp;#x27E9;&lt;/a&gt;</idno>
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            <idno type="stamp" n="LPTENS" corresp="ENS-PARIS">Laboratoire de Physique Théorique de l'Ecole Normale Supérieure</idno>
            <idno type="stamp" n="UNIV-PSUD">Université Paris Sud - Paris XI</idno>
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                    <forename type="first">Kay Jörg</forename>
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                <title level="j">Journal of Physics A: Mathematical and Theoretical</title>
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              <p>In the theory of extreme values of Gaussian processes, many results are expressed in terms of the Pickands constant $\mathcal{H}_{\alpha}$. This constant depends on the local self-similarity exponent $\alpha$ of the process, i.e. locally it is a fractional Brownian motion (fBm) of Hurst index $H=\alpha/2$. Despite its importance, only two values of the Pickands constant are known: ${\cal H}_1 =1$ and ${\cal H}_2=1/\sqrt{\pi}$. Here, we extend the recent perturbative approach to fBm to include drift terms. This allows us to investigate the Pickands constant $\mathcal{H}_{\alpha}$ around standard Brownian motion ($\alpha =1$) and to derive the new exact result $\mathcal{H}_{\alpha}=1 - (\alpha-1) \gamma_{\rm E} + \mathcal{O}\!\left( \alpha-1\right)^{2}$.</p>
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