Intermittency properties in a hyperbolic Anderson problem

Robert C. Dalang; Carl Mueller

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 4, page 1150-1164
  • ISSN: 0246-0203

Abstract

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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. For comparison, we also derive bounds on moments of the solution to the stochastic heat equation with the same linear multiplicative noise.

How to cite

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Dalang, Robert C., and Mueller, Carl. "Intermittency properties in a hyperbolic Anderson problem." Annales de l'I.H.P. Probabilités et statistiques 45.4 (2009): 1150-1164. <http://eudml.org/doc/78058>.

@article{Dalang2009,
abstract = {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. For comparison, we also derive bounds on moments of the solution to the stochastic heat equation with the same linear multiplicative noise.},
author = {Dalang, Robert C., Mueller, Carl},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stochastic wave equation; stochastic partial differential equations; moment Lyapunov exponents; intermittency; stochastic heat equation},
language = {eng},
number = {4},
pages = {1150-1164},
publisher = {Gauthier-Villars},
title = {Intermittency properties in a hyperbolic Anderson problem},
url = {http://eudml.org/doc/78058},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Dalang, Robert C.
AU - Mueller, Carl
TI - Intermittency properties in a hyperbolic Anderson problem
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 4
SP - 1150
EP - 1164
AB - 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. For comparison, we also derive bounds on moments of the solution to the stochastic heat equation with the same linear multiplicative noise.
LA - eng
KW - stochastic wave equation; stochastic partial differential equations; moment Lyapunov exponents; intermittency; stochastic heat equation
UR - http://eudml.org/doc/78058
ER -

References

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