Fractional Brownian motion with multivariate time: persistence exponents
arXiv:2608.26680
Abstract
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
An error was made: an incorrect conclusion regarding the independence of the components of the process's maximum point was drawn from relation (1)