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arXiv · 2608.26680

Fractional Brownian motion with multivariate time: persistence exponents

George Molchan
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Abstract

We consider fractional Brownian motion with D-dimensional time in the domain G(T)=(-T 0 if j<d+1). Let P(T) be the probability that the process will not exceed a fixed level in G(T). We show that for large T, logP(T)=(D-dH)logT(1+o(1)) where H is the Hurst parameter of the process

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George Molchan. 2026-08-27. Fractional Brownian motion with multivariate time: persistence exponents. https://arxiv.org/abs/2608.26680

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