Approximation of the maximum of storage process with fractional Brownian motion as input

Zhengchun Xu, Zhongquan Tan and Linjun Tang

Statistics & Probability Letters, 2018, vol. 140, issue C, 147-159

Abstract: In this paper, the asymptotic relation between the maximum of the storage process and the maximum of the process sampled at discrete time points is studied. It is shown that these two maxima are asymptotically independent or dependent when the grids of the discrete time points are sufficiently sparse or the so-called Pickands grids. The results complete a gap in Hüsler and Piterbarg (2004) which showed that the two maxima are asymptotically coincident when the grids of the discrete time points are sufficiently dense.

Keywords: Extreme values; Storage process; Fractional Brownian motion; Discrete time process (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.05.015

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