Wednesday, July 3, 2019 - 14:00 in V3-201
On the central limit theorem for stochastic heat equation
A talk in the Bielefeld Stochastic Afternoon series by
Lauri Viitasaari
| Abstract: |
We present a quantitative central limit theorem for the
d-dimensional stochastic heat equation driven by a Gaussian
multiplicative noise, which is white in time and has a spatial
covariance given by the Riesz kernel. We show that the spatial average
of the solution over an Euclidean ball is close to a Gaussian
distribution, when the radius of the ball tends to infinity. Our central
limit theorem is described in the total variation distance, using
Malliavin calculus and Stein's method. We also provide a functional
central limit theorem and analogous results in the case of space-time
white noise. Extensions and further open questions are discussed.
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