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On the global maximum of the solution to a stochastic heat equation with compact-support initial data

Mohammud FoondunDavar Khoshnevisan — 2010

Annales de l'I.H.P. Probabilités et statistiques

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...

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