The Problem of Small Unilateral Deviations : the Existence of Decay Exponents

  • G. MOLCHAN
  • Published 2006
Let x(s), s ∈ R be a Gaussian self-similar random process of index H . We consider the problem of log-asymptotics for the probability pT that x(s), x(0) = 0 does not exceed a fixed level in a star-shaped increasing domain T · ∆ as T → ∞. General conditions are given to guarantee the existence of the limit, lim(− log pT )/ψT , for a slowly increasing… (More)