Title: Second order Lyapunov exponent for the hyperbolic Anderson model

Date: 09/14/2017

Time: 4:10 PM - 5:00 PM

Place: C405 Wells Hall

In this talk, I will present some recent results regarding the asymptotic behavior of the second moment of the solution to the hyperbolic Anderson model in arbitrary spatial dimension d, driven by a Gaussian noise which is white in time. Two cases are considered for the spatial covariance structure of the noise: (i) the Fourier transform of the spectral measure of the noise is a non-negative locally-integrable function; (ii) d=1 and the noise is a fractional Brownian motion in space with index 1/4<H<1/2. These results are derived from a connection between the hyperbolic and parabolic models, and the recent powerful results of Huang, Le and Nualart (2015) for the parabolic model. This talk is based on joint work with Jian Song (University of Hong Kong).