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Penalizing fractional Brownian motion for being negative

Author

Listed:
  • Aurzada, Frank
  • Buck, Micha
  • Kilian, Martin

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.

Suggested Citation

  • Aurzada, Frank & Buck, Micha & Kilian, Martin, 2020. "Penalizing fractional Brownian motion for being negative," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6625-6637.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6625-6637
    DOI: 10.1016/j.spa.2020.06.004
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    References listed on IDEAS

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    1. Aurzada, Frank & Guillotin-Plantard, Nadine & Pène, Françoise, 2018. "Persistence probabilities for stationary increment processes," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1750-1771.
    2. Lyu, Hanbaek & Sivakoff, David, 2019. "Persistence of sums of correlated increments and clustering in cellular automata," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1132-1152.
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