On the global maximum of the solution to a stochastic heat equation with compact-support initial data
Consider a stochastic heat equation = 2+() for a space–time white noise and a constant >0. Under some suitable conditions on the initial function 0 and , we show that the quantities lim sup →∞−1sup ∈ln E(| ()|2) and lim sup →∞−1ln E(sup ∈| ()|2) are equal, as well as bounded away from zero and infinity by explicit multiples of 1/. Our proof works by demonstrating quantitatively that the peaks of...