Lower bound for the expected supremum of fractional Brownian motion using coupling. (English) Zbl 07787407
Summary: We derive a new theoretical lower bound for the expected supremum of drifted fractional Brownian motion with Hurst index \(H\in(0,1)\) over a (in)finite time horizon. Extensive simulation experiments indicate that our lower bound outperforms the Monte Carlo estimates based on very dense grids for \(H\in(0,\tfrac{1}{2})\). Additionally, we derive the Paley-Wiener-Zygmund representation of a linear fractional Brownian motion in the general case and give an explicit expression for the derivative of the expected supremum at \(H=\tfrac{1}{2}\) in the sense of K. Bisewski et al. [Electron. J. Probab. 27, Paper No. 129, 35 p. (2022; Zbl 1507.60048)].
MSC:
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60G15 | Gaussian processes |
| 68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |
Citations:
Zbl 1507.60048References:
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