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Fractional Brownian motion with multivariate time: persistence exponents
We consider fractional Brownian motion with D-dimensional time in the domain G(T)=(-T0 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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