Penalizing fractional Brownian motion for being negative

Frank Aurzada; Micha Buck; Martin Kilian

doi:10.1016/j.spa.2020.06.004

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arXiv · 1907.07608

Penalizing fractional Brownian motion for being negative

Frank Aurzada·Micha Buck·Martin Kilian

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Abstract

We study a modification of the fractional analogue of the Brownian meander, which is Brownian motion conditioned to be positive on the time interval ${[0,1]}$. More precisely, we determine the weak limit of a fractional Brownian motion which is penalized -- instead of being killed -- when leaving the positive half-axis. In the Brownian case, we give a representation of the limiting process in terms of an explicit SDE and compare it to the SDE fulfilled by the Brownian meander.

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Frank Aurzada, Micha Buck, Martin Kilian. 2019-07-17. Penalizing fractional Brownian motion for being negative. https://doi.org/10.1016/j.spa.2020.06.004

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