Penalizing fractional Brownian motion for being negative

Frank Aurzada, Micha Buck and Martin Kilian

Stochastic Processes and their Applications, 2020, vol. 130, issue 11, 6625-6637

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.

Keywords: Brownian meander; Brownian motion; Fractional Brownian motion; Girsanov’s theorem; Persistence probability; Processes conditioned to be positive (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2020.06.004

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