Speaker: Le Chen (Auburn)

 

Title: Exact asymptotics of the stochastic wave equation with time-independent noise 

 

Abstract: In this talk, I will report a recent joint work with Raluca Balan and Xia Chen. In this work, we study the stochastic wave equation in dimensions \(d\leq 3\), driven by a Gaussian noise \(\dot{W}\) which does not depend on time. We assume that either the noise is white, or the covariance function of the noise satisfies a scaling property similar to the Riesz kernel. The solution is interpreted in the Skorohod sense using Malliavin calculus. We obtain the exact asymptotic behaviour of the p-th moment of the solution either when the time is large or when p is large. For the critical case, that is the case when d=3 and the noise is white, we obtain the exact transition time for the second moment to be finite.