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2022
- doi: 10.1007/s11134-022-09859-3
- issn: 0257-0130
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K. Bisewski et al., « Derivative of the expected supremum of fractional Brownian motion at H=1 », Serveur académique Lausannois, ID : 10.1007/s11134-022-09859-3
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The H-derivative of the expected supremum of fractional Brownian motion with drift over time interval [0, T] at is found. This formula depends on the quantity , which has a probabilistic form. The numerical value of is unknown; however, Monte Carlo experiments suggest . As a by-product we establish a weak limit theorem in C[0, 1] for the fractional Brownian bridge, as .