Propagation of singularities for the stochastic wave equation

We study the existence and propagation of singularities of the solution to a one-dimensional linear stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. Our approach is based on a simultaneous law of the iterated logarithm and general methods for...

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Bibliographic Details
Published in:Stochastic processes and their applications 2022-01, Vol.143, p.31-54
Main Authors: Lee, Cheuk Yin, Xiao, Yimin
Format: Article
Language:English
Subjects:
Law of the iterated logarithm
Singularities
Stochastic wave equation
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Summary:We study the existence and propagation of singularities of the solution to a one-dimensional linear stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. Our approach is based on a simultaneous law of the iterated logarithm and general methods for Gaussian processes.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2021.09.013