Penalizing fractional Brownian motion for being negative
STOCHASTIC PROCESSES AND THEIR APPLICATIONS(2020)
摘要
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. (C) 2020 Elsevier B.V. All rights reserved.
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关键词
Brownian meander,Brownian motion,Fractional Brownian motion,Girsanov's theorem,Persistence probability,Processes conditioned to be positive
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