Displaying similar documents to “Local sub-Gaussian estimates on graphs: The strongly recurrent case.”

Random walk on graphs with regular resistance and volume growth

András Telcs (2008)

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

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In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space–time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown via the equivalence of the upper (lower) heat kernel estimate to the parabolic mean value (and super mean value) inequality.

Intermittency properties in a hyperbolic Anderson problem

Robert C. Dalang, Carl Mueller (2009)

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

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We study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension 3 with linear multiplicative spatially homogeneous gaussian noise that is white in time. Our main theorem states that these moments grow more quickly than one might expect. This phenomenon is well known for parabolic stochastic partial differential equations, under the name of intermittency. Our results seem to be the first example of this phenomenon for hyperbolic equations....