Boundary non-crossing probabilities of Gaussian processes: sharp bounds and asymptotics

Enkelejd Hashorva, Yuliya Mishura, Georgiy Shevchenko

We study boundary non-crossing probabilities $$P_{f,u}:=\mathrm{P}(\forall t\in \mathbb{T}{X}_t+f(t)\le u(t))$$ for continuous centered Gaussian process $X$ indexed by…