Displaying similar documents to “Extension of the method of quasilinearization for stochastic initial value problems.”

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....

Weak averaging of stochastic evolution equations

Ivo Vrkoč (1995)

Mathematica Bohemica

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A theorem on continuous dependence of solutions to stochastic evolution equations on coefficients is established, covering the classical averaging procedure for stochastic parabolic equations with rapidly oscillating both the drift and the diffusion term.