Integrated fractional Brownian motion: persistence probabilities and their estimates

G. Molchan

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arXiv · 1806.04949

Integrated fractional Brownian motion: persistence probabilities and their estimates

G. Molchan

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Abstract

The problem is a log-asymptotics of the probability that the Integrated fractional Brownian motion of index 0<H<1 does not exceed a fixed level during long time. For the growing time interval (0,T) the hypothetical log-asymptotics is (H(H-1)+o(1))Log T. In support of the hypothesis, we update our earlier estimates of the probability and give analytical proofs.

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G. Molchan. 2018-06-13. Integrated fractional Brownian motion: persistence probabilities and their estimates. https://arxiv.org/abs/1806.04949

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