Survival exponents for fractional Brownian motion with multivariate time

Fractional Brownian motion, H-FBM , of index with d-dimensional time is considered in a spherical domain that contains 0 at its boundary. The main result : the log-asymptotics of probability that H-FBM does not exceed a fixed positive level is (H-d)logT(1+o(1)), where T>>1 is radius of the domain.