Eric Ziebell: Statistics for the stochastic wave equation with Riesz noise based on discrete observations

Speaker
Eric Ziebell, Humboldt University Berlin

Abstract
We estimate the wave speed of a stochastic wave equation in arbitrary spatial dimensions driven by Riesz noise using discrete observations. Based on explicit representations for the covariance function of the solution of the stochastic wave equation, we derive asymptotic normality for an estimator relying on first and second-order temporal increments. Since the wave equation’s regularity depends on the order of the Riesz noise, the minimax optimal rate of convergence based on discrete observations in time at a fixed space point can only be achieved over all regularity parameters based on increments of at least the second order.