Author

G. Molchan

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Preprint Aug 2026

Fractional Brownian motion with multivariate time: persistence exponents

We consider fractional Brownian motion with D-dimensional time in the domain G(T)=(-T<ti<T,tj>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

G. Molchan · 0 citations