Survival Exponents for Some Gaussian Processes

الملخص EN

The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time.

The exponent in such asymptotics is estimated for some Gaussian processes, including the fractional Brownian motion (FBM) in (−T−,T), T≥T−≫1 and the integrated FBM in (0,T), T≫1.