Hyperbolic Anderson equations with general time-independent Gaussian noise: Stratonovich regime
arxiv(2024)
摘要
In this paper, we investigate the
hyperbolic Anderson equation
generated by a time-independent Gaussian noise
with two objectives: The solvability and intermittency.
First, we prove that Dalang's condition is necessary and sufficient
for existence of the solution. Second, we establish the
precise long time and high moment asymptotics for the solution under
the usual homogeneity assumption of the covariance of the Gaussian noise.
Our approach is fundamentally different from the ones existing in
literature.
The main contributions in our approach include the representation of
Stratonovich
moment under Laplace transform via the moments of the Brownian motions in
Gaussian potentials
and some large deviation skills developed
in dealing effectively with the Stratonovich chaos expansion.
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